Given that setup, I would put the P1/P2 and admin controls onto a KeyWiz or I-pac, and the P3/P4 onto a GP-Wiz.
The KeyWiz will run you from $20 for the solder version to $35 for the Max version (that one has screw terminals and keyboard pass-thru).
The GP-Wiz will run you $20, I think.
That setup will let you utilize shifted functions for all your admin keys, so you get a 2 functions/button package.
As long as you don't have any software that requires keyboard input only, or gamepad input only, you should be set right out of the box.
You would need to do a little remapping for the P3/P4 sticks and buttons, but everything else should be set.