you'll want to pull the engine anyway to clean out all the crap that's under the engine tins. if it hasn't been out before you will also find some oil leaks.
you shouldn't be touching the plug wires on a running engine, you'll likely get bit. which means your coils are working fine.
I'm not sure about your 2518, though I recently had a similar experience with my MTD and it turned out to be the brake dragging in reverse.
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JD x475
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