Was the stuck mower a 28"???
The larger pulley is about a 1/4" smaller by my reckoning.
I doubt it will make much difference.
Especially with the motor you are putting on it. I was secretly thinking you could have been over powering the machine, but then you might have some jungle to rectify.
The smaller pulley is 3/8 smaller so that will see the machine go faster. That might work in your favour as with the motor you are getting you will not need to run it at full tilt.
With the spacers. I would assume they are to go on above the pulley to stop the pulley sliding up the shaft. So they would seat on the step on the crank where it comes out of the seal and then steps down to 1" diameter.
a washer under the pulley and a bolt up the centre of the crank to stop it falling down.
Where as the way my pulley was, it had the washer/step in the pulley so it couldnt go up and the press fit of the collar stopped it going down.
Could you please take a couple more pictures of the machine, id like to see what it looks like where the engine bolts on and the 'gearbox'.