Harvest as it is known in the ice machine world is only initiated when your thickness thermostat switches over. If you need to adjust it to get it to initiate harvest then can you leave it at this setting?
What was the reason for changing it in the first place if it harvested on its own?

Other ideas, some long shots:
Does it just need to build up a bit thicker to harvest?
Have you tried to run it all boxed up for a few hours so your thickness thermostat isn't reading any false heat?
Is the white heater wire which works of the arm by the cutter grid stuck on?
Is the new thermostat el cheapo nasty?
Did you fit the new one correctly on the plate with the clamp over it?

The other thermostat (bin) will only send power to the compressor if I recall correctly. From there thickness thermostat will determine cooling or defrost so can't see this is faulty from your description of the error.

Cheers,
Andy.