Engines -
Some added info on JSF gun: What was said publicly when the 27mm was ditched in favour of the 25 mm Gatling, in 2003, was that the issue was life-cycle cost because of introducing a completely new calibre into the US military.
The Gat installation was heavier (as you note, the time-to-rate issue means you need more ammo per burst) but at the time they truly believed that they had positive weight margins.
I believe there was also an argument on the F-35A about the elevation angle (strafe or air-to-air) and I suspect that it was resolved in favour of the former, hence the big bulge over the gun (front end down, back end up).
And finally, since there isn't an available all-purpose round for the 25 mm, they need a new round anyway.
