First, the neighbors: It seems like you have moved out of the property so while its a consideration, its not as much for renting. If it is a major problem, you could be the complaint-making owner" who cares about the community and neighborhood. You could be the squeaky wheel for noise and physical pollution.
The property: I would say, you have to be clear on what your goals are. Grow your portfolio? Grow your cash flow? 'Bank' more capital gains? Knowing where you want to head might lead you to a decision. But once you sell a house that has appreciated well in value, it's gone. Good or bad. You could refinance it or lease option it to a tenant. They would take on the risk of the neighbors and more of the headaches associated with the area.
Really my point is that whether you refinance it or get a HELOC or lease-option it, its easier to make the decision you're facing when you have a fall-back; Easier to buy something else when money is coming in already. And if after you buy something else, you still want to get rid of the property, you still can.