I built a second set of circuits using MC78L05ACP regulators in a T092, and powered them up using a 9V battery.
When I checked the outputs with no load (each powered separately), I found 1.9mv of noise on the non-poly cap circuit, and a 26mv 2.5khz oscillation with the poly caps.
The in-circuit measurements are:
Non-poly circuit Output to GND: 4.5uf ESR=0.73 ohm
Poly circuit Output to GND: 5.58uf ESR=0.10 ohm
Non-poly circuit Input to GND: 95.66uf ESR=0.12 ohm
Poly circuit Input to GND: 186.0uf ESR=0.02 ohm
I'll add some loads next.