It seems that popular opinion on this forum is that some FTC time is a necessary step in a good pork shoulder cook. After doing a lot of pulled pork both ways, I think FTC does nothing good for taste or texture. The bark gets soft, and the meat can over-cook and get mushy.
For me FTC is only a tool for holding meat that comes off egg too early. If I want the very best pulled pork I try to time it so it comes off the egg with about an hour or so to rest uncovered. Once it cools to 150-160, it's ready to pull. I think the biggest mistake I you can make is pulling it when it is too hot. Pull it when its too hot and all your moisture steams away leaving you some nice dry pork.
If you haven't skipped the FTC step in a while, try it and see if it does not make a better sandwich.