I did something similar last summer. My Craftsman LT1400 uses the standard 500cc Briggs motor and that motor has some tragic design flaws that make it grenade itself roughly once a season. I went through a couple of these motors rebuilding them (correctly) until I gave up.

I ripped the tractor down the the frame and removed most parts. Got $40 Ryobi walk behind mower motors (42V which is really 36V), some scooter controllers, and pulleys. I used two scooter Li ion batteries but I should have just gotten three large lead acid 12V batteries for more capacity. Still, I can mow for an hour or so and get almost an acre done which includes some hills per charge. It took about 8 total days to build and about $800.

The way I set it up is that I have one motor drive the wheels and two more motors on the deck directly driving the blades. The belt system the ICE motor version had was insanely inefficient. This system has like 20% of the power but mowed better and is way more reliable. For $150 I could get a solar array and controller to charge the batteries and never pay for anything but belt and blade replacements for life.

The hardest part of the build was lining up the mounting of the drive motor and wiring up all the safety systems (brake sensor, seat sensor, etc). The kicker is that this is a way better product than what I can buy commercially unless I get into the $5k+ territory and is completely user serviceable. No part here is more than $100 and they all readily available. The tractor has enough torque to push my huge picnic table around while I am riding it. I might try seeing if I can plow snow with it next winter.