Full disclosure, I'm a CA mortgage broker and have my hands in both conforming and private money, and most of my clients are investors.

I currently owe about +/-$60,000 on it with a traditional, conforming mortgage.

The furlough will not count as a gap in employment but you will not be able to get a conforming loan until you begin receiving pay stubs again

I don't see many (if any) on a cash-back refinance or when the subject property is a rental.Loans that are above the conforming loan limit ("jumbo" loans), and other portfolio programs have different rules and may require an interior inspection.

According to https://www.nerdwallet.com/blog/mortgages/va-home-loan-limit-and-funding-fee-changes-2020/:"Loan limits will still apply in 2020 to veterans who have one or more active VA loans or have defaulted on a previous loan...Those VA loan limits are the same as the ones set by the Federal Housing Finance Agency on conforming loans.

HI @Ed Kowalchuk, If you're willing to close with the loan in your name and transfer title to the LLC after closing, you can get a conforming at a 30 year fixed rate.

Of course the rate won't be as low as a conforming conventional as these type loans typically start around 6% or even higher with no experience.You didn't mention price or market so don't know if you are talking about an $80k property or a $200k plus duplex.

Use the hml to buy a property that wouldn’t qualify for a conforming loan, fix it up, then refi into a conforming loan.

Maybe a private lender...Either way, its can't be a conventional conforming loan since you can't show proof of being able to repay the loan.  

You may want to check their lease to make sure it conforms with state law.