When I first became a landlord, I ran into the same hurdle. I was actually trying to move to Nashville, but I couldn't sell my house in Utah because the market had crashed and I was upside-down on my mortgage. But being stuck with that mortgage wouldn't allow me to get another mortgage due to my poor debt-to-income ratio. But I really wanted to buy another house, and I was determined to make the cross-country move to Music City. So I found renters for my place in Utah and hit the road.
When I was searching homes online, my mind was blown by how much lower prices were in Tennessee, compared to Utah. And on top of that, this was 2010 (right at the bottom of the crash). So I took all of my life savings and bought a house (maybe more of a shack) for $18,600. Unfortunately, it was uninhabitable, and I still had to rent a duplex with my friend for a year while I got that paid-off shack livable.
Over that year of paying rent at the duplex, I had those Utah tenants paying rent to me every month, and when I was able to prove that income on my tax returns (and when I got a good steady job in TN), I was able to qualify for my second mortgage.
But now, instead of buying my second house, I would actually be buying my third. So I got a mortgage and got a house closer to the city, and I rented out that little shack of a house for $700/month.
So, though it may not be preferable, you could move into an apartment and rent out your house. Then, once you have a year's rental income on your tax returns, you should be able to get a new mortgage and get out of the apartment and into your second home. But in some instances, a signed lease agreement could possibly be sufficient proof of income also. Not sure what the details are on that. It's always VERY beneficial to talk to lots of different lenders.