Hmm... for mumble, as of mumble-1.2.4-227-g1bd57bd, I have been able to start Mumble before SWTOR without SWTOR crashing. The overlay appears in SWTOR if Mumble is started first. This is using Windows 8.1 64-bit.
I use Mumble all the time, and just to add to this: you can start Mumble after running SWTOR and still get the overlay, but you have to do it before hitting the [Play] button after logging in.
If you start Mumble after hitting [Play], the overlay won't work. You have to quit out of SWTOR and restart it to get it working.
The Ventrilo overlay will work as soon as Overlay is enabled, regardless of program start order.