I would look for an old race frame with a "euro" bottom bracket. that's a standard BB for road/mtb. it will be the best thing to make it compatible with a double-ring road crank.

the hard part will the chain tension. you can't put a rear derailleur on a bmx bike easily. you might be able to use a der hanger from a cheap bike with semi-horizontal dropouts. also, how do you plan to put cable stops on the frame for the FD?

I think your best bet is to get a long bmx frame (a 21" top tube is considered pretty long) and run it as a single-speed with a tall seatpost (qr clamp for ease of storage) and some tall bars and run it as a single-speed. bmx frames are spaced at 110mm, so a 130mm road hub or 135mm mtb/hybrid hub will not fit in your frame. the FD fitting will be even more difficult.