Should I get lucky enough to gain another property, I may also attempt to rent out my primary home after the refinance, and BRRR the next property. 

FHA borrowers must move into the home 60 days after the mortgage closes and must keep it as a primary residence for at least one full year.Sep 23, 2021https://www.investopedia.com › askCan FHA Loans Be Used

They're failing at one of their primary tasks and they're not communicating with you to explain why they're struggling or how they will resolve it.Time to move on. 

You should only have a homestead exepmtion on your primary home. 

Try this; if you have a mortgage on your primary and a car note, tell that finance company you cant pay because Uncle Rodger broke his leg and his kids are starving.

The 1400 sq ft single family home next to our primary has been a rental for the last 8 years or so and part of a large portfolio with a professional management company and their tactic is to professionally landscape once yearly and put grass and snow removal on the tenants, so I know it's done both ways locally.

My beautiful wife was awarded a settlement, which we plan to use to buy a SFR as a primary.

What is the strategy and primary use for this property? 

He says that there are low money down lending opportunities that exist for people who intend to live on the property as their primary residence.

That's funny, the same thing actually happened to me at our former primary.