It is likely that the app will be built against, minimally, the new versions of the system libraries, and there may be new OS level interfaces that it needs as well. I would say there is little to no chance it would run even if you could find a way to get a stand alone copy.
I agree about waiting for a new version to settle down before installing. I only upgraded a week ago. It has settled down, and I have had no issues, and it is indeed a superior OS version.
The last couple of upgrades to OSX have been more about increased stability and performance than wizzy new features, and they have been pretty happy experiences. It was when they removed Rosetta support that everyone got upset, because old PowerPC only applications ceased to work. That wasn’t caused by problems in the new OS, it was caused by an explicit choice by Apple to delete a feature.
The question of constantly paging and being slow sounds like there is an application that is badly busted. Mavericks adds a new feature to its memory management - compression of in memory data, and this generally reduces paging - and gives you the effect of a significant increase in apparent memory. It may be that on systems with limited memory it gets into a pathological state. Check the memory use with the activity monitor - and see if there is an application that is chewing a lot of memory, or if there is something else odd. Firefox is the usual culprit for generally leaking memory, but this sounds different.