Still think that an SOT-23 package is a bit small for 50mA with a 7V drop.
For a small increase in $$ an SOT-89 or SOT-223 package regulator would be a better choice.
You can not get much heat out of the SOT-23 or SOT-23-5 regulators due to the small leads.
That may be why they just provide the junction to ambient number in the data sheet.
The larger tab on the SOT-89 and SOT-223 gives them a better heat transfer to the plane, and you want one that has a ground tab, not a input or output tab like some regulators..
I am not sure the low noise aspect of the AP2210 would make much difference here.
Maybe its just my aerospace background taking over here, we usually did not have much room for temperature rise...
As far as the input noise is concerned, I tried a 3dB attenuator at the input and that did not help, so I would assume a high value resistor would not help either.
I found that with at least one nylon standoff the input was stable with no signal..
The board was OK with three of the ground connected standoffs but the 4th one initiated the noise problem.
It was quiet on the bench.
ed