And if so, the 1031 would have to be for a "third" (or more) property equal to or more of the value of the selling price, correct?

I highly recommend getting a photographer who specializes in STRs.

You are mentioning highly sought after parts of GA.I do commercial real estate over 20 years now specializing in NNN properties.Don't expect monster cash flow here for residential.

For example, you could just refi what it owed with a conventional or DSCR loan using the new value right now with a 30 year fixed.

I received an update from my accountant and it seems the timeline of events did provided some clarification and reduced my taxes by $6k from the original $16k. 

and my stocks as you well know are highly liquid as well. 

If you are planning on buying it with a smaller down payment, that will also increase your mortgage costs as you are borrowing more and also need mortgage insurance.The price of the home (from the seller's perspective) is based on market value and condition, not on whether or not it matches the 1% rule.   

Purchased for ~$20k under market value.

Last year I paid cash for an 8 unit value add that initially wouldn’t qualify for financing.

Once you're comfortable, then you can dive into value-add opportunities or the BRRRR strategy.