Unless you are really good ( I mean really, really good..) at fabricating lots of little parts and making them work well together, it's a big long-shot. Is it an overhung style crank weedeater? They are generally the worst engine for durability to try and make work with a friction drive, because you subject the engine's main bearings to a lot of side loading they were never designed to handle. Of course you see lots of them done home D.I.Y. designers on Youtube, but you never hear of them running for lots of miles in use.
I'd be looking for a used GEBE or Stanton drive kits with engine, you will pretty much know that they will work with minimum of fuss.
Besides I doubt that getting replacement parts for the Remington weedeater would be easy, and most times people are trying to sell them because the lawn and garden repair place said they couldn't fix it. They should be giving you this engine, for the trouble it possibly could be fixing it up.
Caveat Emptor.
