Virtual Persistent Maps / Tabletops?
I played games of Diplomacy here, where the GM uploaded a map to a thread, then he would update it and re-post in the next message. This gave us a set of maps showing the history of our game, with the last map being the current map.
It should be possible for each player to copy such a map, host it for themselves, modify it, and re-post it as the new current map in a new message.
Not exactly what you were looking for, perhaps, but maybe a workaround - and it has the advantage of creating a movement history, in case you need to check back.
The GM should take copies of all posted maps, of course, in case a player host fails for whatever reason.
Alternatively, can images be posted in a Game Wiki? I've never used one, but I believe they are editable by anyone.