An ambitious project. I have done several 3 and 4 axis mills and routers and find those to be pretty simple. I have also done one lathe with a C-axis and live tooling, no Y axis or sub-spindle. It was an order of magnitude more complex than any mill I have done. I think a 7 axis screw machine would be challenging, but not impossible.
Depending on your budget constraints, I would be looking for a machine that uses servo motors/drives that do not use a proprietary communication protocol to be compatible with LinuxCNC. In other words, simple analog control with the loop closed at the controller. This eliminates the need to replace the servos. Above all, look for a mechanically good machine.
A Citizen L20 might be a good choice. Good parts availability, and there are a lot of those machine out there.
Given your background, I don't think you'll have any problem accomplishing your goal. But it certainly will require some tweaking of the LinuxCNC software to make it all work.
I'll be interested in seeing your progress.