Do they make what you are talking about, or is it something you'll have to create? I've heard/seen the cable floor shifters, never one that kept the stock shifter on the column.
I'm sure it would eliminate coming out of gear if it is related to frame flex. You'd have to be careful and have help, but you could try running without the linkage at the transmission hooked up, see if the problem goes away to confirm that is indeed the problem.
Another thing comes to mind, is your linkage actually all there? I don't deal with automatics much, but as I recall there is a spring and plastic piece that are part of the linkage near the transmission, those being broken or missing could cause problems.