Sorry to hear of the bad luck!

Agreed, sounds like the Doo Hickey may have come apart. This is always the first thing KLR riders have to fix on that bike ... before taking a long journey.
The KLR is not common in Mexico, but if you get a good mechanic, you may get out of this. It mostly likely can be repaired ... but as you've said, parts will take time to get hold of.
I read a report of a French guy stuck in Oaxaca with a DR650, had a broken gear box. Parts were sent from Suzuki in Mexico City, repaired and he was back on the road in about a month, according the report. He had an EXCELLENT mechanic.
Find the very best guy you can, go on the KLR forums and find used parts for repair.
I don't know if Kawasaki has dealers in Mexico City, they might have. ???
Have someone send parts via DHL or FED EX. Be sure to include a receipt with parts or they will be stuck in Aduana. You will have to pay duty, so have them write the receipt for LESS than actual cost (if possible). It should look "official".
No idea about parting out a KLR down there. Few on the road there, so basically worthless to locals unless it can be made whole again and running ... which, IMO, is your best option other than just walking away.
1. find best mechanic you can
2. determine if it's repairable and what parts are needed
3. find out if Kawi has dealer in Mexico City
4. Search BIG KLR forums in USA to get help getting parts and advice.
(KLR.net)