The thing about condos is the HOA will go up and your mortgage stays the same so you will end up losing by the end of the mortgage. 

Looking for a house we could house hack, had an incredibly low interest rate on mortgage and house has increased in value about 42%, an estimated 180k in equity.

Yes, the lender was Premium Mortgage.

You should to talk to @Andrew Postell He is the best mortgage guy for this.

Purchase price: $320,000 Currently have a long term renter, the rent pays the mortgage and other expenses but provides no cash flow.

They also could have a mortgage that could not be satisfied by the price and in that instance, again the bank would not release it - so again stuck. 

Probably 8%+ mortgage interest at 40% down to make a safe assumption.

I mean myself and any bank would need more details, but if you utilize that large sum as a downpayment and have a small mortgage, wouldn't you easily qualify for the debt to income?

For the $525K property, with the low mortgage rate(you will probably never get a such low rate), it might make sense to hold onto it for now, especially if you can still sell it as a primary residence within the next three years and avoid capital gains taxes.

All LP equity gone.Even before interest rates took a huge jump: property bought with 75% LTV first mortgage, pref equity up to 90% LTV, and funded last with LP equity.