Also worth noting that he took out a reverse mortgage on the home before he passed away. 

The basic rule for the amount of cash to have at hand is 3 months of ALL expenses as if the rental was unoccupied and you had to pay all the utilities on top of the full Primary mortgage, Interest, Taxes, and Insurance (PITI).As well, it's pays to have a bit more because life happens.Good Luck!

Don't do it, severe penalties for not following proper procedures.

The rough plan in my head has been to move to Jacksonville and buy a house between 400k-500k with cash so we don’t have a mortgage.

So, essentially through the lender I had lined up, they would cover literally 100% of the costs of EVERYTHING, but it was a cheap house with low renovation costs, so the interest payments were not going to be any larger than a typical mortgage payment around here.

You wouldn't be able to "add" a property since they are already under one mortgage note. 

Are you losing money on a monthly basis (cashflow) or are you upside down on your mortgage?

Is there a way for  TIC to accommodate this requirement so I avoid the mortgage boot?

Traditional investment mortgage.

I commented on another post recently where the website says "secured mortgages" which is what the sponsor invests in, but when you read the fine print your investment is unsecured.