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Are there any ways to use the equity that don't have brutal rates?

A 6%+ annual appreciation rate is decent. 

Super low vacancy rates in SD, even STR's. 

So, what is happening today is not as important as what will happen in the foreseeable future.If rents are increasing faster than inflation (I use 5% per year as an average rate), then it may be worth holding the property, since your cash flow will increase as rents rise.However, in your post you stated, "Mortgage rates have kept increasing as well, that's why I put a range on negative cash flow."

I was also getting credit card balance transfer offers at 0% promotional rates for a year to a year and a half and I started transferring my HELOC balances to the promotional credit cards.

There are options to work with the title company after purchase (60 days) to buy it with conventional financing and then shift the property into an LLC with a quitclaim deed to get the same effect as purchasing with your LLC but you get the advantage of better rates with the conventional loan.

However, if the FHA interest rate is lower, I would still go that route and if rates drop refinance  however keep in mind FHA has PMI for life  Here you go

You could negotiate terms such as a lower interest rate or interest-only payments for a set period to ease your upfront burden.Lease-Option Agreement: If the landlord isn’t ready to sell outright, consider proposing a lease-option where you continue renting for a set period with an agreed purchase price.

Some will tell you to make the change anyway but that seems a large risk in this high interest rate environment.