There are some 3% down conventional loans with lower PMI rates. 

I have rental income in 2018, too, but that's obviously not on a tax return yet.I don't think either bank was interested in a HELOC against either my existing rental property, or my residence... they were trying to send me through the conventional mortgage route.So... what is my next step? 

I also explored the option of doing a ReFi on one of our VA Loans to a conventional loan so we can free up our VA loan to utilize it again for our follow on 4 plex however, the lender that I spoke to told me that we may run into issues doing that as well.

Banks are overflowing with cash reserves.The problem is that housing inventory is extremely low.

Then the work will begin.The HomeStyle loan is ONLY for Single Family Homes.Other Important Items to Know about “Conventional” Renovation LoansMaximum – Minimum Purchase/Upgrade Amounts:Minimum: $ 5,000 (below this on an exception basis only)Maximum: Limited to 50% of the “after improved” valueOccupancy: Primary, Second Homes, Investment PropertiesRenovation Term: The renovation term for this program is a maximum of 180 days.The Borrower(s) is responsible for the work being completed within the escrow period.

@Sean Cole  its regional for sure.. the ones I had in MS and AL  feed us the deals.. but lots of deals there ... its funny as we talk about this.. some parts of the country there are still plenty of deals others its very tight the deal ship has sailed and its basically pre 07 market.. one size does not fit all.in Oregon we have little to no OREO inventory anymore all those agents that specialized in it are out of business and back to doing regular real estate.. the foreclosures at court house that were 20 to 50 a week are down to 3 or 4.. with MASSIVE competition.. it all cycles that's for sure.. but I bet you can still roll into certain big cities and buy hang over inventory..

Do you know if your client qualifies for conventional financing?

I recently quit my W-2 Job an am now having difficulty being approved for even a small conventional loan and looking for advice or tips. 

And, we can't qualify for a conventional loan until later this summer due to our past mistakes...

But some time if you have higher score its good to go with conventional loan because you may get lower MI depend on your loan scenario.