I've been building agent-doc [1] to solve exactly this. Each parallel Claude Code session gets its own markdown document as the interface (e.g., tasks/plan.md, tasks/auth.md). The agent reads/writes to the document, and a snapshot-based diff system means each submit only processes what changed — comments are stripped, so you can annotate without triggering responses.

The routing layer uses tmux: `agent-doc claim`, `route`, `focus`, `layout` commands manage which pane owns which document, scoped to tmux windows. A JetBrains plugin lets you submit from the IDE with a hotkey — it finds the right pane and sends the skill command.

For context sync across agents, the key insight was: don't sync. Each agent owns one document with its own conversation history. The orchestration doc (plan.md) references feature docs but doesn't duplicate their content. When an agent finishes a feature, its key decisions get extracted into SPEC.md. The documents ARE the shared context — any agent can read any document.

It's been working well for running 4-6 parallel sessions across corky (email client), agent-doc itself, and a JetBrains plugin — all from one tmux window with window-scoped routing.

[1] https://github.com/btakita/agent-doc