The factory 4-speed is called the RAD. It is the same behind all 4 engines used in the MII (other than gearing differences). Other 4-speed choices might be the T-10 or the Top Loader from the early Mustangs, however these would require modifications to the MII bellhousing/flywheel/clutch, and possibly the
trans tunnel.
Your best bet is a T-5 5-speed transmission from a late-model Mustang. Modifications are required for this swap also, but at least you get a 5-speed with OD for your effort. There are two paths...use the MII bellhousing/flywheel/clutch with minor modifications, or use the late-model bellhousing/flywheel/clutch with a rebalanced flywheel and stock exhaust manifolds. In either case, the
trans mount has to be shifted rearwards and the shifter opening in the
trans tunnel must be opened forwards. At least your AT driveshaft should be the right length when you use the T-5 yoke from the donor car.
Check the Tech sections of both
The Mustang II Organization and
Mustang II Network - 1974 - 1978 Ford Mustang II for more details.
The Cobra seats in the MII are just the "deluxe" seats available in all MII's. You can check for nice restored examples and color swatches on both of the above sites.