How do I adapt my spiral ratcheting screwdriver to use with all bits?
I'd try to join one of your existing bits to a 1/4" socket. Maybe the slot will fit nicely into the 1/4" drive side of the socket? A bit of file work should get you to something pretty firm. Then apply liberal amounts of 2 part epoxy and you should be good. (Bonus if you can find a thin rare earth magnet to sit in the bottom of the socket to hold your bits better.)