I am thinking about other houses, that in So. Carolina and in Las Vegas. There is a chance that at least one of them has been turned into Airbnb and looks much better than his Long Island house. BTW, he said he was handy, so I think the lack of interest in the family house indicates something (unhappy with the family situation and in denial? Distracted by something else?)
However, all his classmates said that he was definitely very smart. It seems that some of his clients got irritated with his perfectionism, but others, liked it and valued his expertise.
So, obviously he is not a stupid man. As such, he has to understand that a lot of bodies in one neighborhood sooner or later might converge on the perpetrator. Logically, if he hunts near his lair, he probably would move to one of other houses and hunt there.
Now, I don’t know where his So. Carolina house is. If it is Charlotte or a touristy place in the vicinity of Hilton head, he won’t stand out. If it is in more rural area, he’d probably not hunt there. Las Vegas and Reno are full of tourists and sex workers, so, quite possible.