Use the sander. You’re refinishing anyway. I wouldn’t use chemical strippers. I do probably half a dozen or so refinish jobs a year. Your first grit with the drum sander is # 20. Very similar in looks to gravel driveway glued to paper. It will take your padding, whatever is left, and your glue off without any problems. You may go thru a couple of belts but I would be very surprised if you used more than two. Just my thoughts. Good luck