I certainly know that future years the expenses won't remain that low, but wouldn't that be a reality on a property that has a lot of recent improvements?  

Rates as low as 7.25, depending on credit score and LTV.

Your thesis is basically rent low and accept less desirable tenants so I don't think that is the best thesis to base an investment off.

The profit was used to buy a higher quality SFH in the same area.

Question: assuming an ideal brrrr that has all investment extracted at the refinance, why would you choose a low cost market over a high cost market?

Too many low income apartment buildings near by / vacant buildings. 

My thought is to use a HELOC for the down payment on a new property (20% down), then once I acquire it, do a cash-out refinance to pay off the HELOC while keeping my original low rate intact.

If you can’t do a 1031 to a non-income tax state, figure out a year when you will have lower income and tax rates ar as low as possible.

No syndication experience but there are about a dozen quality RV/Mobile home parks on market in Oregon, several with owner carry options that can be passiv-ish with management in place.

Find a quality agent in Texas, then ask them if they offer a referral fee.