You probably have thought of this already, but.... Inside the fixture is a 1 inch by roughly 3/8in thermostat. If the fixture becomes over heated it cuts the fixture off. I believe I read somewhere on the web that if it is tripped you have to replace the fixture or at least the thermostat. Anyway the conclusion was that an electrican had to be called if you are not a DIYer. The voltage check gets me. But the incandescents don't work, so you may not be getting the power you think.
Do a search of the web. You will find that this is a common issue.
I did alot of testing on CFL bulbs to determine the heat produced. The manufactures say that the fragile computer in the bulb which we know as the ballast has a very critical temperature range. So I got out a thermometer and measured the heat in a number of enclosures. I was shocked at how high the temperature got even in an open bulb. The incandescents get 3x hotter, but the temperature in one open cfl bulb inside the coil was hotter that the max allowable by the manufacturer of that cfl bulb. Now that was nuts. No wonder everyone says that the bulbs burn out so often. If you have a lot of time, go to HD, buy a Halo fixture, if you can safely do so, wire the new unit to a cord. Next insert the bulb and measure the heat. Check on the web to see the heat level which will trigger the safety thermostat.
There are ways that you may be able to get the heat away from the can, like perhaps a flector cfl type bulb which is approved for recessed light (Lowes and HD now have them). There are 23 watt CFL refectors on the internet if you want them. Also a light manufacture told me, and I am not telling you to do this, but he said to get the heat away from the ballast, drill 3 holes at the top of the can if it does not have insulation contact.

I am getting ready to install recessed lights but because of this whole issue I am checking "Title 24 Recessed Lighting Housing HB6PLRIC-26-E-AT-AD" fixtures. There are many types available which can be seen at www thefind.com/homefurnishings/browse-remodel-ic-compact-fluorescent-housing

These fixtures have bulbs separate from the ballast. The ballast is not in the heat. And the bulbs are cheap. But the bulb is not coiled. Has anyone seen or used these?
Thanks,
Bob