Hey, @Samantha Elliott. Great question!
Let me summarize what I understood and please let me know if I am off base:
You are moving and currently have a property with a great interest rate, strong rental market because of military base, and 15 years left on the mortgage. You are going to be moving out of state and want to purchase a new home in NE and keep the current property as a rental. The issue you are trying to solve is getting the cash in hand to purchase the new home, potentially looking at a financial product to access the equity in the property? Sound about right?
The first questions I would ask are:
What term loan is your current property? If it was a 30 year with 15 years left, that amortization schedule for your principal balance looks a lot different than if it was a new 15 year mortgage.
Are either of you active duty or a veteran who is eligible for a VA loan? You probably would have mentioned if you were, but worth the ask.
Are both of you listed in the mortgage and deed? There are a lot of programs for “first time home buyers” out there right now, which pretty much means all you need to qualify is meet the IRS definition which is essentially cannot have owned and occupied your primary residence for the past three years. Again, probably not, but worth the ask.
Where I am going with all this is, have you looked into low down payment options that you all may be able to qualify for and afford without having to use an additional financial instrument on the rental property? Keep in mind, if that property is rented, you should be able to use a portion of the rent for your debt to income calculations.