What do you mean by “gets stuck”? Does it skip back into the same groove over and over or does it literally get caught (that would be horrible)?
For tough gunk, I’ve found dabbing a microfiber cloth in ultrasonic cleaning fluid and wiping with a lot of pressure along the groove is the best way of getting rid of this gunk. I had this issue in the past when I was using a silicone roller to pick up dust from the records, which at some point started to deteriorate and leave silicone in the grooves. That’s the reason those types of cleaning rollers are now discontinued.