Would a home equity loan be a viable option in this situation, especially in regards to eliminating some of the red tape I'm running into with a refinancing an scorp-owned property?

You could trim your expenses by eliminating property management - you can absolutely do this yourself on a 6-unit, even as a newbie.

That would minimize and maybe eliminate the need for a loan for those properties.

Eliminate debt, establish a budget, and save.

Fix it.We eliminate as much landscaping as possible: we take out flower beds and most decorative features, ideally, lawn mowing is the only job tenants have to do, because we know that's all we can expect from most.

Using a 1031 to upgrade to a two-family could help you reduce or eliminate the $1,000 out-of-pocket expense you’re paying now.Also, condos often come with HOA fees that limit cash flow, so be mindful of their impact.

If I put 10% down, with on time payments, I’ll have 20% equity in about a year or so, eliminating mortgage insurance.

I am in the process of getting it reappraised to eliminate PMI.

That helps you eliminate properties but not decide what to buy.   

Real Estate is THE BEST way to decrease/eliminate your tax burden.