Fix for Greasy Pulled Pork?
I doubt that your meat is really greasy. If it is really overly fat, you will notice it when buying it, your meat will be marbled through and through. But it is difficult to get such meat nowadays at all, since it is rather expensive to produce. 

The mouthfeel you describe is more likely to come from the gelatine. When you make pulled pork in the pressure cooker, you are converting the connective tissue to gelatine, leaving the overcooked muscle fibers swimming in it. When warm, it is really slippery, and the meat slides around in it - this is exacthly what makes for proper pulled pork that shreds. And making gelatine from collagen is not that easy. Traditionally people tried to convert as much as possible by very long cooking times, but using high pressure is much more efficient. So it is likely that you are ending up with more gelatine, or better hydrated gelatine, than with traditional cooking. 

The first thing you can try to do is to just learn to like it. There is nothing inherent in greasiness which makes people sick eating it, that's a learned aversive reaction, which can be unlearned. With the knowledge that it isn't actual fat, that reaction can subside or disappear. You can try some mindfulness meditation on some bites of the meat to get accustomed to the mouthfeel too. 

If you insist on reducing the sliperiness, you might have to make your process less efficient. This means going to a more traditional stovetop recipe without pressure. I don't know if your exact InstantPot model can cook in slowcooker mode without pressure, but if it can, you can keep the convenience of set-and-forget. You will probably have to live with other changes in texture though, not getting such a nice separation. 

Gelatine loses its gelling strength with low pH. So you are on the right way with sour sauces. You can try to marinate it with them, and keep a sour sauce in the pot while cooking it, not just adding it at the end. But then you will end with more of a braised meat, which you might not like. 

In general, it is difficult to give more advice, because this is exactly what makes your pulled pork good pulled pork. Anything you do to disrupt it will lower the quality of the texture you get.