Chris, maybe it is just me but this seems to be a bit confusing. You said you tried two tts on the side wall, "directly opposite the firing of one of my speakers". Does this mean one speaker is toed-in to such a degree that it is aimed at one of your tts?
Now perhaps a few points were suggested in my earlier comments that were not made clearly.
First, it is not always easy to differentiate between airborne and structure borne vibrations. After I moved my tt, it was then located in a position with less structural bracing (likely bad), yet it sounded cleaner. So in my case I must infer the minimizing of airborne interference was a net gain over the increase in structure vibrations.
Second, I think a lot can be understood about equipment location from the study of speaker interface with the room. It seems to be understood that where three planes intersect (any corner) you will find the greatest build up of bass nodes. (Insert assumption that bass frequencies have more energy, thus are more detrimental than higher frequencies.) While the corner of my alcove may not have been as severe as a room corner with longer walls, my experience (two shorter walls and a large shelf = three planes) still supports this point. Less of a problem with bass node build up may be realized where two planes meet -- two walls, a wall and floor or ceiling. Further reduction occurs with only one plane (along a wall and up from the floor) while the least airborne interference may be away from all walls and the floor, while admitting this may be the least practical.
I believe this also relates to Jim Smith's recommendations in "Get Better Sound" when he promotes side wall equipment locations over front wall between the speakers.
Conclusion: try locating your tt/arm/cartridge where there will be the least bass node build up.