Thanks for all the input. I ended up taking a torch to the carrier for a couple of minutes and then spraying a bunch of release-all in there. I think it got sucked in by capillary action. I then proceeded to ratchet it out for the next 10 minutes, occasionally applying more release-all. It finally came out so I cleaned it up with the dremel with a brass wire brush and cleaned out the carrier with some brake cleaner and a .30 cal bore brush that I have. I lubed up both pins and put it back together and the caliper now slides easily...but I couldn't get the piston to go back in. I have the special tool and I even opened the bleeder but it just wouldn't budge. Looks like I have to replace the caliper now, unless there's some way to fix that. Has anyone been able to recover a caliper that is stuck?
On a side note, I live in Canada so the whole brake carrier looks like it's been at the bottom of a lake for the last 10 years. The dust cover that goes around the rotor is gone, but I can still see rusty remnants of it around the bolts that used to hold it on. Salt really destroys any exposed metal quickly.