IMHO adjust your expectations, accept you can’t afford to live on the mountain, find the next best thing, and focus on that.

Unless that property has been gutted and renovated a couple times over the years, there's likely a lot of issues that conventional lending and insurance won't accept and will require you to fix within the first year of ownership. 

If offer is accepted, inspect property.7 - If property inspection shows actual rehab needed "plays nice" with analysis rehab, then buy property,  If actual rehab isn't what you instructed your REA to ONLY bring you, then withdraw the offer.This takes far less time for the REA since I'm only making inspections on properties I like. 

You can do a 5% down conventional loan for a owner occupants and not deal with FHA loans (harder to get accepted but not impossible).

I accept complete responsibility for allowing this to happen and not nipping it in the bud.

But that is like in any international destination at the moment because of Covid and the Riviera Maya (including Cancun) is probably one of the least affected areas as it is one of those that accept visitors and on of the very few that accepts American visitors.

I am worried that after the offer gets accepted, the appraisal value might come in significantly lower than the contract price.I understand that discrepancies happen, and I’m not concerned about a small gap (10-20k), however, if the appraised value would come in significantly lower (50-100k, or more), then I would simply not be able to afford this property (given my then lower down payment, and worse mortgage interest rates).I am wondering if anyone has any experience with what happens in such cases?

1 You start an LLC.  2 Fund the LLC with the money you need for earnest money.3 The offer is made by the LLC, with you as the representative member of the LLC4 - If the offer is accepted, you sell the LLC for your assignment fee plus the earnest money you put up5 - The LLC closes on the property with the new owner of the LLC as the new rep6 - You get your assignment fee from the sale of the LLC7 - You are no longer affiliated with the LLC8 - There is no paper trail to your assignment fee that is visible to the seller. 

We close next month and will immediately start accepting applications and screening tenants. 

What lenders will do however is accept previous tax history for future income once you own the property for a year or two so if you wanted to refinance later you could do that.