Re: It's time...
a friction drive mite work on the back, would probably require some modding to make it work.
as for inframes, you said you can probably fabricate anything you'd need.
i know that bike well, its an older style GT performer, i had one for a long time, great bike. but i can tell you for sure no HF or chinagirl motor will fit in the frame.
you mite want to look in the DIY section and make a weed eater, it will let you cruise around 15-20 on flats, you'd have to help pedal up hills to get that speed but it wouldn't be too bad.
weed whacker motors are small enough where it mite work, i know it has been done, although i'm not sure how reliable they were or much of the details.