So you’re stuck with a problem. if you have a good real estate agent that wants to help you, that person will request proof of payment ie bank records showing the tenants pay regularly … but I’m no expert. 

There are a few banks that offer lending, but the terms are terrible.

The bank I'm getting the loan from requires insurance to be in place prior to closing.

Speed of Financing: Time is crucial in fix and flips, and traditional loans (like bank loans) can be too slow.

If you're going for non full documentation loans then there are other methods to qualify as well (rental income/ bank deposits/profit and loss/no income/etc) but these loans have higher rates and costs typically.

I am trying to purchase a few properties in bank foreclosures and looking for an affordable way to do a title search.

Besides traditional banks to access the equity via HELOC or refinance, what other programs are there via private lenders that will allow me to access that equity?

You can close the loan in an LLC so that when you file the 1st year you can pay all payments out of your business bank statements and it will not go against your DTI for future home purchases or refinances.

As you grow, more banks will want this from you. 

At this point, I would recommend having a line of credit to cover these things so you don't have money sitting in the bank doing nothing when it could be put to work.I have 33 units, no debt except for mortgages, and excellent income.