So I spent the day working on this, believe it or not, making a bit of a science project out of it. I was able to resolve the same problem by just stripping the slides down, removing my filters and transitions. Then I tried the gentleman's solution here, using the stabilizer, which resolved the bad transition issues but still left me with some shaky slides. I stripped them down again, still with the stabilizer on all, and this time added de-interlace filters for the ones from faster moving footage, rendered, added the transitions, rendered again. This looked quite good on the tv. Finally, I tried another round, this time stripping it all back, removing even the Stabilizer filter, and added just the De-Interlace filter where needed, (plus the basic border filter stripped back to just one frame line to clean the edges). Render. Then add the transitions. Rerender. This looked just fine as well, and spared me the sluggish render time when putting transitions over "stabilized" slides.
So it appears that the solution to the shaky transitions was more about the order in which the filters are applied, rather than the Stabilizer filter per se. So long as the filter is applied and rendered before the transitions are applied and rerendered, it turns out ok--the stabilizer isn't the key, but the order. Thanks for your solution, it put me on the path to mine!