The speed issue is why having everything constantly synced across, like DropBox or SugarSync, is probably the best approach. FTP, VPN with drive mapping, or any other tech is going to be way too manual, slow, and annoying IMHO. But then I'm still not sure I really understand the original requirements...
DropBox, SugarSync, and others can appear as regular drives on your system, accessible by all apps using the normal file system. While these systems also of course cannot make the transfers go *faster*, the simple fact that syncing is done automatically and in the background means it's likely that when you need a file in both places, it will already be there, instead of having to wait on a file transfer done manually.
- Oshyan