I did a loan for a woman that owned a Christmas tree lot, she made all her money in Nov and Dec, and didn't work the rest of the year.

The two solutions towards the top of my list (selected as an industry neophyte) are Buildium and AppFolio. 

The solution to me seems to be periodic cleaning of the closets, but the tenant wants me to “fix” it.

These loans and the process, level of scrutiny and costs associated with them, are geared for longer term solutions to hold real estate.

I'll be curious to hear your chosen solutions. 

Until family gets involved we would accept checks from this person and then work with family to find the best solution for all.

The next several months were extremely stressful; the tenants left, I watched my bank account get lower by the day, and I spent every waking hour trying to figure out a solution. ...for weeks, I thought I was headed for bankruptcy, and I assumed the entire house would need to be razed (who would buy a house that has regular, unpreventable floods?).

@Tim Herndon I appreciate your solution oriented answer.

This is a backwards solution but if you become pet friendly you can full your units and not have to deal with applicants. 

Easy Living Housing Solutions.