If it's unlikely or impossible to get a HELOC, what is our next best option to borrow against rental equity?

Not accurate.The industry would stop moving if all issues were 100% resolved before proceeding.

Being able to borrow money at 3-4% for a business is very powerful and unique. 

Here is my situation - I own 2 properties outright that are positive cash flowing right now and I tried borrowing or COR one.

I don't yet have final numbers on loan amount and terms, but even if the story stopped here I consider it a success.

I have a primary borrower.

If, hypothetically, I lend $400K unsecured and my borrower disappears off the grid, I will have a huge loss.

(financial things)..to include but not limited to any new leases or modification of existing leases together with rent rolls, with respect to borrower financial conditionThanks for your time

I would not touch the 401K, but I would stop putting money in it so you can have cash for renovating your new investment property.

In my limited experience with portfolio loans, lenders typically use mostly the same criteria that a bank would use for traditional financing, but will allow a borrower to go over 10 loans if their finances justify it.