My experience is limited to folded cascode circuits like Earth. I have less experience from standard opamps like Moon or complementary amps such as Sun.
Improvements on Earth will make it an AD797-clone.
The simple SK170 input stage sounds warm and fuzzy and nice in a way but not clean. It's not obvious everyone would like "improvements" here, but cascoding improves details and soundstage. The sound is leaner with a more forward presentation. CFP is an alternative and also improves details and make it leaner.
SA970/SC2240 sound hard, typical solid state. To my ears SA1016/SC2362 are better.
A bipolar input stage might sound better but introduces problematic bias currents that has to be dealt with. My favourite input stage at the moment is bipolar CFP.
Applying a floating current mirror and shunt transistor to the folded cascode stage as in AD797 make it sound much better without compromises. Just cleaner and more enjoyable. I think many would describe it as "space around instruments" or "blacker background".
It's a couple of more transistors, but I think it's worth it. I don't think the basic folded cascode circuit can compete with the best monolithic opamps, and why do discrete opamps that sounds worse when they're larger and more expensive, often draw more current and have worse output swing.
To be discovered: if cascoding the folded cascode improves things, if the combination of cascode and CFP is as good as I hope, how a cascoded bipolar input stage sounds