As Emily Litella would say--That's very different. Never mind... Sorry, I misunderstood you.
I really think pillowtops should be illegal. Of course I'm being facetious, but they are just the worst things ever invented to sleep on. They sag almost immediately and are usually so overpadded with soft, soft foam that you just smother in them if you can sleep at all without your back killing you from lack of support.
I know you're reluctant to perform surgery on the mattress, but I think that might be the only real solution. And really, what have you got to lose other than a lot of sweaty sleepless nights? I think someone on the forum reported on removing a pillowtop but I'm not sure if I read it in the new forum or the old one. You could search.
Putting anything over the pillow top--even a very expensive wool topper is only going to give you more to sink into. Then you'd be smothering in foam and wool besides. Removing the pillowtop is the only way to go. I think you can make your current mattress work for you by modifying and customizing. If you don't care for latex or MF there are other kinds of high quality foams like HR, which you can get in a variety of ILDs to suit.