Moped/motor bike project

I got an old moped with no rims and a dead motor. I came across a free 20" bicycle and cut it up to bolt the pedals in. I don't want to cut the frame but can't afford moped parts so I'm looking at putting on one of those Ebay 80cc kits on the thing. I plan on building some kind of bolt on frame to hold the motor just behind the front tire if it looks like it will fit once I can afford a motor kit. Then I have to come up with some kind of front break. It's the dead of winter, 2 feet of snow here, so I thought this would be a fun project. Now if only I wasn't poor. Any thoughts?

The moped is an 1984 tomos silver bullet, but it shares many parts with Punch. The moped army isn't much help as I live in Minnesota and they don't have much of a presence here. I could ship the parts but money being an issue and all I figured doing it as a 20" bike with suspension would be a cheap way to get it riding until I can afford the parts as nothing last forever anyway. The main thing is to not ruin the moped parts I have while trying to get it going. I have other bikes I could put a motor in, but I really think this would be fun. I was going to put a smaller sprocket on but I think the extra power is worth the lower speed to extend the clutch life as has been pointed out might be an issue. I am considering changing the sprockets and pedals so I can get the thing up to speed. There is a ton of help for bicycles around here, even free bicycle parts but every time I mention adding a motor people say "why don't you just pedal?"

This thing is a three way love child...

The motor was seized and covered in RTV silicone. I had to hammer the piston out because it was siliconed to the walls. The cylinder walls are shot (rusty pitted), the rings broke and there isn't a gasket in the whole motor. I left the moped at my parents and my dad says he gave away my rims and tires to a guy so he could make a trailer. The cables and wires are all shot from sitting outside. I got the front shocks to work but the rear ones are frozen. I recovered the seat with a leather jacket from the thrift store for $4. I rewired the lights to a battery and have been riding it as a bicycle (it's not that heavy).

I love the comment of you could build it cheaper by using just a bike, that being said I hope you finish it. I got quite a smile out of that. It's an interesting thing, I'm glad people are interested. Thanks guys!