It is critical that you have an evaporator matched to the higher 15-seer condenser. It is very important to have a (TXV) or thermostatic expansion valve refrigerant metering device on the new evaporator. Most 15-seer rated coils will have a TXV.

It only is important for the air handler to deliver 400-cfm per ton of cooling. If it is a 3.5-ton system the air handler will need to deliver with, a wet E-Coil, 1400-cfm or more. The delivered CFM should be checked.
There are several ways to check the CFM delivery check out the links provided.

You will need a good HVAC Tech to do this work!

- Darrell

Here is a link that might be useful: Correct Sizing of Residential Air Conditioning Systems & Ductwork Systems

Thank you Darrell, I am going to investigate this further.

The compressor I have now runs OK but makes this awful sound when it shuts down, my HVAC company tells me there isn't much they can do to fix it -- so my interest in replacing it.

You need to replace the coil and variable-speed air handler (furnace) inside to get high SEER ratings. Your utility company may not acknowledge just a half replacement because there is likely no data available to prove it gets 15 SEER.