(Though the arbitrage is very attractive)I'm now considering a 1031 exchange, but then (correct me if I'm wrong) I'd have to get a new loan to cover the loan I'm leaving behind...

Many OOS investors set themselves up for failure because they don't truly take the time to understand:1) The Class of the NEIGHBORHOOD they are buying in - which is relative to the overall area.2) The Class of the PROPERTY they are buying - which is relative to the overall area.3) The Class of the TENANT POOL the Neighborhood & Property will attract - which is relative to the overall area.4) The Class of the CONTRACTORS that will work on their Property, given the Neighborhood location - which is relative to the overall area.5) The Class of the PROPERTY MANAGEMENT COMPANIES (PMC) that will manage their Property, given the Neighborhood location and the Tenants it will attract - which is relative to the overall area.6) That a Class X NEIGHBORHOOD will have mostly Class X PROPERTIES, which will only attract Class X TENANTS, CONTRACTORS AND PMCs and deliver Class X RESULTS.7) That OOS property Class rankings are often different than the Class ranking of the local market they live.8) Class A is relatively easy to manage, can even be DIY remote managed from another state.

Conventional mortgage loans do not carry a Occupancy requirement which makes it attractive to investors. 

As long as it is at or above your mortgage balance, you will actually be making money each month if you break even on the sale (plugs the hole in your wallet).Another option is to contact your tenants and see if they would like to buy the house.

From what I understand their business model is getting paid by the banks and the banks so far are offering it free of charge to attract clients and stay competitive.

They are often not even there - they are out looking at attractions, theme parks, etc. 

These "off the books" loans are very valuable so I will pay a little more to the owner to make it attractive enough for them to offer it.

Focusing on how to attract longer term (permanent) tenants will net 200% more (incrementally) vs any other tactic IMHO.tips:   buy the book  Landlording on autopilot. 

Simple cash repayment horizon is 3.3 years, and attracting better quality tenants at the higher price point.

Not the attractive answer than anyone wants to hear but if you want it bad enough you’ll make it happen.