What is the typical load resistance for a thermostatic circuit?
I don't see why you would not just leave the bucket switch in place and ignore the overflow switch in the pump. It performs the same function (shutting off the compressor), just at a higher fill level. That seems to be how it is intended to be used. 

If you want to add to the bucket switch (I see zero reason to replace it) you could use the microswitch in the pump to switch the relay to interrupt the power. There is no need of a resistor, if you have a 24VAC relay and a 24VAC transformer. The specifications of that relay appear to be adequate to switch the compressor (18A 277VAC) directly. It may not have a very long life switching a compressor load, but it should never actually actuate unless something is wrong. 

Pump microswitch (from manual in your link):


Whatever mains-voltage wiring you do on the contact side of the relay (if you should decide to go that way), as well as the transformer primary, has to be kept enclosed, away from water and done to an appropriate standard to be safe.