I am not sure what your doing wrong because Remedy makes my Bowling Balls Cover tackier than any cleaner I have ever used including Lane Masters and Clean N Dull.  I also have no problems with it removing oil rings.  It won't remove your track.  I use it by hand no spinner spray, sit, wipe.

Either you have unrealistic expectations (you're not going to be able to just wipe the towel across the ball with zero pressure once and expect it to do much, you gotta use a little elbow grease, preferably with a microfiber towel), you're doing something else completely, totally wrong, or you're full of s***.  There's no way Remedy won't at least get the oil rings off your ball if you're using it properly.  Spray it on the ball, let it sit for a few seconds, and scrub it down with a clean microfiber towel.  Repeat if necessary.  It WILL get oil off the ball and leave it feeling tacky.  Period.  Whatever you see left on the ball surface is probably just the track that gets marked up on the ball, not a puddle of oil sitting on top of the coverstock.

I just can't understand it because you are literally the ONLY person I've ever seen who couldn't get Remedy to get the oil off their ball.  Heck, I once used it on a buddy's ball when he left it in the car all week and it sweated out a thick layer of oil all over the entire ball.  And I STILL was able to get the oil off and leave the ball feeling tacky in two minutes with several sprays of Remedy and a towel.