Don't think that you need that specific motor. It is a very nice motor and it is made for what you want to do. However, others can be used, so keep an eye out if you're looking to save money.
Also, you don't need a motor with a 1" shaft. Chances are your motor is going to spin at a different rpm than the gas engine anyways so you'll need to buy new pulleys for it to get the drive and mower deck to spin the correct rpm. Since you're replacing the pulleys you can have whatever motor shaft size you want.
If you're really looking to do a budget based build, it is going to take time to collect the parts as they come along at a reasonable price.
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