Under the FHA rejecting a person for the ESA dog is a form of discrimination against those with disabilities.Your post suggests that this person has passed all your screening criteria except for the ESA dog.

Personally, I'd never buy the biggest house, or the most expensive house on the street.

Quote from @David Eyal: This is actually very simple: don't get involved in personal issues.You offer them a renewal.

I have locked up one deal off the application and have offered in person on 2-3 other deals.

you mention the person who is complaining is now and living in an efficiency unit (to me that has everything in it-ie fridge, stove). 

I will say that if you get some ducks in a row, things like a good cleaner, handy person etc, you could manage from farther away if you find a deal or area you are interested in.

"Also, if a person can demonstrate sufficient education or job experience showing his professional knowledge of unregistered securities, he too can qualify to be considered an accredited investor."

We took this approach because even though the house is an STR it is also one we want to use as a family a couple times per year, and we feel we have our own personality as hosts, so we were particular about what we wanted. 

I gave them a lease in person to review and sign (I gave them the lease first as they mostly speak Spanish and the lease is in English, so I wanted to give them the time to read it).

Unless there is an offer deadline, I personally think order of offers has influence on sellers.