I've been having trouble starting my '05 XA in colder temperatures the last two months. It starts but is very shaky and will stall unless I keep my foot on the accelerator for about 20 seconds. The lights dim a bit without the accelerator down.

I had the battery replaced. Problem continued.
Spark plugs replaced and tune up. Problem continued.
Throttle cleaned. Problem continued.

One shop said it was probably a coil pack issue, and a second shop said that wasn't true.

They did point out that the EVAP sensor on the air filter housing was broken, but that it is such an expensive fix and they could not replace it at the time anyway.

Any other suggestions?

It's a valve that's mounted on the air filter, not a sensor. A broken one may cause a vacuum leak but that would be happening all the time, not just on start up.
Try cleaning the idle control: http://www.clubxb.com/forums/showthread.php?t=42924

The shop wrote me up a quick description of the EVAP problem. It's actually the wiring that is broken ("VSV EVAP wiring.") They advised me to bring it back to whoever may have broken it, but who knows when and where that happened.

There's no cleaning "broken," just expensive replacement. I'm not even sure if that would fix the problem if I did have it replaced.

Post a pic of what's broken if you can.

Actually the check engine light just popped on. P0012..