diff --git a/app/src/main/docker/claude-eval/Dockerfile b/app/src/main/docker/claude-eval/Dockerfile
index b586dd9d..ebaf1cc9 100644
--- a/app/src/main/docker/claude-eval/Dockerfile
+++ b/app/src/main/docker/claude-eval/Dockerfile
@@ -13,10 +13,16 @@ FROM debian:bookworm-slim
 # git: Claude's own Bash tool calls `git`; the worktree's .git points back
 #       into the main repo object store, both mounted from the host.
 # curl + ca-certificates: the native installer downloads over HTTPS.
+# python3: plugin MCP servers and hooks run Python (e.g. sphinx's server,
+#          which needs >= 3.11; bookworm ships 3.11).
 RUN apt-get update && apt-get install -y --no-install-recommends \
-        ca-certificates curl git \
+        ca-certificates curl git python3 \
     && rm -rf /var/lib/apt/lists/*
 
+# uv: plugin launchers (e.g. sphinx-mcp.sh) use `uv run` to install their
+# pinned Python deps on first start. Installs to ~/.local/bin (on PATH below).
+RUN curl -LsSf https://astral.sh/uv/install.sh | sh
+
 # Claude Code native build. The install script places the launcher at
 # ~/.local/bin/claude and the versioned binary under ~/.local/share/claude.
 # Runs as root in this image, so HOME=/root.
diff --git a/app/src/main/java/app/drydock/agent/providers/claude/internal/ClaudeEvalContainer.java b/app/src/main/java/app/drydock/agent/providers/claude/internal/ClaudeEvalContainer.java
index 30cab8f3..274140f5 100644
--- a/app/src/main/java/app/drydock/agent/providers/claude/internal/ClaudeEvalContainer.java
+++ b/app/src/main/java/app/drydock/agent/providers/claude/internal/ClaudeEvalContainer.java
@@ -10,6 +10,7 @@
 import java.nio.file.attribute.FileAttribute;
 import java.nio.file.attribute.PosixFilePermissions;
 import java.nio.file.attribute.PosixFilePermission;
+import java.time.Duration;
 import java.time.Instant;
 import java.util.ArrayList;
 import java.util.Comparator;
@@ -27,6 +28,7 @@
 import app.drydock.agent.api.EvalTokenResolver;
 import app.drydock.process.ProcessResult;
 import app.drydock.process.ProcessRunner;
+import app.drydock.process.ProcessTimeoutException;
 import app.drydock.state.json.JsonParseException;
 import app.drydock.state.json.JsonParser;
 import app.drydock.state.json.JsonValue;
@@ -100,7 +102,9 @@
  * {@code --settings}/{@code --mcp-config} flags resolve unchanged and the
  * host-side activity watcher keeps reading the same files. The personal
  * config mounts are read-only (see above); everything else is writable
- * because the session owns its state there.</p>
+ * because the session owns its state there. One named volume is shared by
+ * all eval containers as {@code XDG_DATA_HOME} (see {@link #DATA_VOLUME}),
+ * so plugin installs made on first start outlive the container.</p>
  *
  * <p>All methods are blocking and must be called off the JavaFX application
  * thread. {@link #probe} is run once at provider init (background) and its
@@ -114,6 +118,15 @@ public class ClaudeEvalContainer {
     private static final String IMAGE = System.getProperty(
             "app.drydock.eval.claude.image", "drydock-claude-eval:latest");
 
+    /**
+     * Named volume shared by every eval container and mounted as
+     * {@code XDG_DATA_HOME}, so what plugins install there on first start
+     * (e.g. sphinx's uv venv, about a minute to build) persists across
+     * sessions instead of being rebuilt in each fresh container.
+     */
+    private static final String DATA_VOLUME = "drydock-claude-eval-data";
+    private static final String DATA_VOLUME_PATH = "/var/lib/drydock-eval-data";
+
     /**
      * Managed-settings locations, in precedence order (macOS first, then Linux).
      * Resolved per call (not cached at class-load) so a test can point the
@@ -287,6 +300,9 @@ public Optional<EvalSetup> mark(String sessionKey) {
         if (sessionKey == null || sessionKey.isBlank()) {
             return Optional.empty();
         }
+        // A container left behind by a crash (no unmark) would make this
+        // launch's `docker run --name` fail on the name conflict.
+        removeContainer(sessionKey);
         Path configDir = stateDirectory.resolve("eval").resolve(sessionKey);
         try {
             Files.createDirectories(configDir);
@@ -306,12 +322,16 @@ public Optional<EvalSetup> mark(String sessionKey) {
         return Optional.of(setup);
     }
 
-    /** Reverses {@link #mark}: deletes the per-session config dir and drops the stash. Idempotent. */
+    /**
+     * Reverses {@link #mark}: removes the session's container, deletes the
+     * per-session config dir and drops the stash. Idempotent.
+     */
     public void unmark(String sessionKey) {
         if (sessionKey == null || sessionKey.isBlank()) {
             return;
         }
         setups.remove(sessionKey);
+        removeContainer(sessionKey);
         Path configDir = stateDirectory.resolve("eval").resolve(sessionKey);
         try {
             deleteRecursively(configDir);
@@ -320,6 +340,31 @@ public void unmark(String sessionKey) {
         }
     }
 
+    /** The {@code docker run --name} of {@code sessionKey}'s container. */
+    static String containerName(String sessionKey) {
+        return "drydock-eval-" + sessionKey;
+    }
+
+    /**
+     * Force-removes {@code sessionKey}'s container, if one exists. Closing a
+     * session's terminal kills only the {@code docker} client; without this
+     * the container keeps running with its mounts indefinitely.
+     */
+    private static void removeContainer(String sessionKey) {
+        String name = containerName(sessionKey);
+        try {
+            ProcessResult res = ProcessRunner.run(List.of("docker", "rm", "-f", name), null, Duration.ofSeconds(15));
+            if (res.exitCode() != 0 && !res.stderr().contains("No such container")) {
+                LOG.log(Level.WARNING, () -> "Could not remove eval container " + name + " (exit "
+                        + res.exitCode() + "): " + ProcessRunner.excerpt(res.stderr()));
+            }
+        } catch (IOException | ProcessTimeoutException e) {
+            LOG.log(Level.WARNING, () -> "Could not remove eval container " + name + ": " + e.getMessage());
+        } catch (InterruptedException e) {
+            Thread.currentThread().interrupt();
+        }
+    }
+
     /** The stashed setup for {@code sessionKey}, or empty if {@link #mark} has not run (or failed). */
     public Optional<EvalSetup> setupFor(String sessionKey) {
         return Optional.ofNullable(setups.get(sessionKey));
@@ -373,6 +418,9 @@ public String wrap(EvalSetup setup, String innerCommand, Path worktree, Optional
 
         Path mainRepoRoot = resolveMainRepoRoot(worktree);
         StringBuilder cmd = new StringBuilder("docker run --rm -it");
+        // Named after the session key (mark() names the config dir after it)
+        // so unmark() can remove the container.
+        cmd.append(" --name ").append(shellQuote(containerName(setup.configDir().getFileName().toString())));
         cmd.append(" --add-host=host.docker.internal:host-gateway");
         cmd.append(" -e ").append(CONFIG_DIR_ENV).append('=').append(shellQuote(setup.configDir().toString()));
         cmd.append(" -v ").append(shellQuote(setup.configDir().toString()))
@@ -387,6 +435,8 @@ public String wrap(EvalSetup setup, String innerCommand, Path worktree, Optional
                 .append(':').append(shellQuote(hooksDir.toString()));
         cmd.append(" -v ").append(shellQuote(activityDir.toString()))
                 .append(':').append(shellQuote(activityDir.toString()));
+        cmd.append(" -v ").append(DATA_VOLUME).append(':').append(DATA_VOLUME_PATH);
+        cmd.append(" -e XDG_DATA_HOME=").append(DATA_VOLUME_PATH);
         // The config-dir symlinks (mirrorPersonalConfig) resolve against the
         // user's ~/.claude, so it must exist in the container at its original
         // host path -- read-only, so a container session can never mutate the
diff --git a/app/src/test/java/app/drydock/agent/providers/claude/internal/ClaudeEvalContainerTest.java b/app/src/test/java/app/drydock/agent/providers/claude/internal/ClaudeEvalContainerTest.java
index 177a4752..a93e4ce6 100644
--- a/app/src/test/java/app/drydock/agent/providers/claude/internal/ClaudeEvalContainerTest.java
+++ b/app/src/test/java/app/drydock/agent/providers/claude/internal/ClaudeEvalContainerTest.java
@@ -179,6 +179,11 @@ void wrapWritesTokenToFileNotArgvAndDropsDoubleSh() throws Exception {
         String imageAndAfter = cmd.substring(cmd.indexOf("drydock-claude-eval:latest"));
         assertFalse(imageAndAfter.contains(" sh "), "no extra 'sh' after the image (entrypoint is already sh)");
         assertTrue(imageAndAfter.startsWith("drydock-claude-eval:latest '"));
+        // Named after the session key, so unmark() can remove the container.
+        assertTrue(cmd.contains(" --name 'drydock-eval-sess' "), () -> "container named after the key: " + cmd);
+        // The shared data volume backs XDG_DATA_HOME, so plugin installs persist.
+        assertTrue(cmd.contains(" -v drydock-claude-eval-data:/var/lib/drydock-eval-data "
+                + "-e XDG_DATA_HOME=/var/lib/drydock-eval-data "), () -> "shared data volume: " + cmd);
     }
 
     @Test