Update: Ordered a 12V wall wart described as "linear" and the noise is unchanged. Went through a drawer of wall warts and tried ~8 with no luck.
Decided to find one with screws in the case and see about bypassing the electronics so it would just be AC output from the transformer, then see about running that through a rectifier and regulators as needed. But the one I opened looked like this:

Looks like stepped down AC output goes to four diodes and a filter cap. Am I missing something or is this the basics of a linear supply? Because when I put it back together and plug it in, I still get the noise.
This is aging me.
Decided to find one with screws in the case and see about bypassing the electronics so it would just be AC output from the transformer, then see about running that through a rectifier and regulators as needed. But the one I opened looked like this:

Looks like stepped down AC output goes to four diodes and a filter cap. Am I missing something or is this the basics of a linear supply? Because when I put it back together and plug it in, I still get the noise.
This is aging me.