Allow me to rephrase the facts in your question: You want to move to a different area because you do not like the school system or the tax rate. You want to keep the house and turn it into a rental. You have less than 25% equity in the house. You have a good credit score you want to maintain. I infer you cannot afford another mortgage because you mentioned you cannot include rental income on the property because there no rental history.
You need to set your priorities. What is your single top-most priority? Is it moving? Renting the property? Maintaining a high credit score? You are at a standstill because you are trying to keep three priorities as No. 1 and there can be only one top priority.
You have several solutions. The most obvious is sell the property. That way you preserve your high credit score, free yourself from the mortgage payment, and liberate equity you can use to buy a property in a county with low taxes and excellent schools.
Or, rent and move into a residence in a county with low taxes and excellent schools for two years during which time you build a rental history on the property you own.
Another solution is to become involved in the school district to affect the changes in the school system that you want to see accomplished. Alternatively, attend county supervisor meetings and understand where and why your tax dollars are being spent so that you can speak out to your representatives about the local tax rate.
The least desirable solution is to default on the loan and walk away from the property, especially if you have equity in the property. A foreclosure will free you from the property, but at the expense of, among other things, your credit score.
However, if you have no equity in the property, consider a short sale.
I hope this information helps you Find. Learn & Save.