Greg,
This is a tricky one. But it sounds like your bike is good to go if the brake is working, not dragging and not leaking fluid. So I think you're fine for your Mexico trip. Worry about fixing things when you get back. Rear pads should last 10,000 miles or so. I would do some riding and using the rear brake to make sure all is OK. No leaks? Good to go.

A good machinist can probably extract the old broken Easy Out. Or maybe you can do it without destroying the caliper? Be careful. Most time, tapping the Easy Out will loosen it and it will fall out and be able to be pulled out.

Once you remove the broken easy out, this is what I would do:
First, soak the broken bleed bolt with WD40 or Penetrating oil and let sit over night.

Buy or borrow a SNAP-0N (or other HIGH QUALITY) Extractor to pull out the stuck bolt. Good technique in the use of this tool makes all the difference. If you are not sure what you're doing, let a machinist do the job, or good mechanic. Experience counts on this one.

You risk destroying the Caliper, but no big deal, lots of used ones on Ebay for cheap if you need another.

Bleed bolts are notoriously brittle and kind of get corroded and welded in place. That is why it broke. You need to bled your brakes more! Twice a year is good! Moto brake fluid absorbs moisture and becomes ineffective.
Change twice a year! Better braking, less fade!

Good luck, just take it easy and slow. Think about what you're doing.