Op-amp rolling is obviously the easy stuff to try, should also bring noticeable differences to the sound.

LM4562 are very good but need care to get the best out of them, their also not much good at driving capacitive loads

Did you ever try the NE5532 instead of the JRC4558 Stan? I know the 5532 is frowned upon by a lot of people and classed as old tat but they are actually capable of decent results

Of course they don't have the speed,bandwidth, ultra low noise as some of the newer types but they are cheap, DC offset can be higher but used on a single rail with DC blocking caps it shouldn't be a problem

For the more expensive so called Audiophile grade theres AD8620, AD8065, LM4562, OPA2132,OPA2134
All of those should work on a single rail, theres lots more that could be tried too