could be that these KoolStop pads were made for the Modolo PRO style holders which are different (AFAIK) to these holders you have. I don't have one in front of me to pull apart for for one the PRO holders and pads are rounded on the leading end and square-cut on the trailing end. plus the fitting is a bolt rather than a nut and is designed to screw into a threaded boss (tubular) on the holder and might be smooth on the holder inside, The longer bolt is made to go into the hole in the pad for extra security.
I assume KS does not offer a "rounded on both ends" Modolo pad, so if this is your only choice you might need to carve a groove into the hole so this pad with press in. but if you do be SURE you always position the pads/holders correctly since "slip-out" will be much more likely!
I'd use a burr in a Dremal is I was going to do such carving, and lock up the pads in a small vise