Also, the banks won't finance it as a two family or count any income. 

Because so many people commit mortgage fraud to get that 1% difference in interest rate bank underwriters have gotten strict on additional purchases within a local commuting area.

I was exploring a heloc as well but I have not contacted a bank about that option. 

Some banks will not accept the Non-NFIP policies.

The seller aka bank will permit the potential buyer to contact the local utilities and have them put utilities into the buyers name for one day for the inspection which of coarse is a contingency that you’d arrange as part of the sale .

I had recently just refinanced our two-flat to get out of the PMI using a major, big name bank.

I got a showing right away and realized with the occupancy at 35% and deferred maintenance there is noway I could get bank or agency financing.

Personally, I never really have vacancy, although we under write for it & plan for it at ~5% of Revenue ( bank standard here with my bank ) we have yet to have an apartment sit vacant.

I can't imagine in any jurisdiction and definitely not in Texas that a landlord can bar a tenant from accessing the unit based    On a police report or any other evidence for that matter.  

What are some of the most established or reliable banks out there to put money into a higher interest yielding savings account?