Paynes can be fine if installed correctly. Why would he replace the outdoor unit and not the indoor unit? In some states that's illegal. It's called mismatching and actually hurts performance, overall, more than just leaving it alone. 10 SEER and 13 SEER together give you about an 8-9 SEER rating. Don't do it.
The new refrigerant is R410a and is replacing R-22. 410 is a HFC and 22 is an HCFC. The HCFC has the chlorine atom that kills the ozone. The HFC just has a higher global warming potential. The HFC requires the linesets to be clean (not necessarily cleaned) of the older oil to a point of <5% of total system oil charge. It's better to just not have any as it doesn't mix to well but per DuPont <5% is acceptable. The newer refrigerant is more efficient but, at this time, more expensive. It also requires better handling, cleaning and instillation procedures than R-22 did.
DuPont Refrigerants - Suva® 410A - Are You Prepared for the HCFC Phaseout?
DuPont Refrigerants - Freon 22 - Are You Prepared for the HCFC Phaseout?
It sounds like to me you need to call someone else. Who cares about the "top" 20... The top 20 of what? The ACCA? ASHRAE?
Seriously, message me and I'll get you to someone in your area or point you in the right direction to find someone in your area...