Wow.
That's some nice equipment. If you don't mind me asking, how exactly did you get such an awesome grant?
If you have any details like tooling/CAM software/feeds and speeds or parts you make, could you share them with us?
I would likely take the CNC lathe before a 4th axis. All I've ever seen teams use their 4th axis for is hex shafts or jobs that only require a few indexing moves. You could likely just put an indexing table with tailstock in your 3 axis mill and put in pauses in your program to let you rotate the part.
The CNC lathe can actually be a pretty useful machine if you know how to program for it. I don't know the specs for this specific machine, but the Haas lathes are usually pretty powerful.
Again, it all depends on the team.