[..] save. When running in project mode TM seems to stat every file in the
project  when it regains focus, which results in much slowness
especially over  VPN connection. When using these remote volumes, [..]


Hi, you might want to try this plug-in http://ciaranwal.sh/remate/ that allows to disable the refresh that TM does when regaining focus.

I use it a lot when working on projects that are not located locally on my machine but on others (especially smb shares) over the network.

Hope that helps.

Edoardo Galvagno