Diversion (or: a challenge to Tim: what are you doing this weekend?!). Cassini: "...is, in a nutshell, an HTTP server written in C#. It's fully HTTP/1.1 compliant... it's all open-sourced, free to the public, and weighs in at 10 files, 7 core classes, and less than 50K of total source code". The core webserver is only a handful of lines. Plugging this into a Groove tool should be very straightforward. Decouple it from the filesystem (because filesystems, generally, stink); and have it serve streams directly from your shared space. Roll-your-own "edge services".

Honestly, this is the "easy bit" (because it avoids the issues of cross-firewall access, multiple-devices-for-one-identity, intermittent-connections). But I've not seen it done yet.