I got stuck in a deal like this last year. A friend had a B112 of his dads that sat in a barn for 20 years. He just wanted it running and cleaned up , no paint. Rusty gas tank , crapped up carb, bad belts, stuck valve, flat tires, no spark... etc. The first thing I asked him was "what is your budget?" He said $1000. After fighting it for a month, he picked it up and payed me $1000. $500 for parts, $500 labor. I quit counting at 100 hours. Hard to find a mower shop to work on your crap for less than $5 an hour
I would do something similar to this^^^ Sometimes you just have to eat some time. You did part way get yourself into this so I say just eat some time and do it right if its possible. The biggest problem I see is the missing/wrong parts. You will probably enjoy working on it so that will help some.