I definitely understand your conundrum, but if the rental payment of $4k/mo is barely or just covering the mortgage/escrow expenses, then its not really a good rental. I completely understand it wasn't bought with the intention of being a rental, so I'm not at all criticizing you for having it. But if you're trying to evaluate it objectively as a financial investment, its a poor one.
A good long term rental property that's intended to cashflow (and not just bought on speculation/appreciation) *should* rent for enough monthly to not only cover the mortgage, but also allow you a % to save for capital expenses/repairs, maintenance, property management, periods of vacancy, etc. and then have some profit leftover to pocket. Have you read about the 1% rule? While not hard and fast for every RE market, its a sensible back-of-the-napkin calculation to help you know if your rental is likely cashflow positive or not. If your property can't command 1% of the purchase price in monthly rent, it likely can't cover itself in terms of expenses like repairs, management and have positive cashflow. If you purchased at $750,000 and its getting $4,000/mo in rent, its not even close to meeting 1%. While the mortgage will be covered in the best of times when its rented, periods of vacancy or costly repairs will put the investment underwater in terms of it making you any money.
I'd sell it to be rid of the headache and the risk, esp before vacancy rates begin going up. If there's a depression/downturn in the next 24 months, it'll be hard to find a renter at $4k/mo, AND your selling price would be even lower than you're being quoted now. I guess it depends on your risk tolerance, but I suspect you might sleep better at night if you got rid of it.