You know this is a Tom Petty song, right?

As a commercial underwriter, I’ve rarely seen a private or institutional lender forgo a loan policy.

This is like the Kenny Rodgers song "You gotta to know when hold them, know when to fold them, know when to walk away and know when to run." 

Escrow is set by law and you cannot forgo it (no matter the down payment) if that is what your lender requires for this type of loan.

However, first ask yourself what your intent is for going in the first place is.

Last I knew, you could add reasonable fees for going into the process of eviction to a tenant's bill (double check this).  

Or forgo the primary residence refi all together and just take more equity out of the first rental property to buy the second? 

I'm not saying that either option is wrong, but I will say that a surprising number of investors on BiggerPockets forgo option B when it makes way more sense to go with option B in their neck of the woods.There is always a tradeoff - do you want cash flow now, or the possibility of far better returns down the line?

If it comes back positive you should be able to get the property for a song. 

Is there a better option for going forward as an investor?