OK, so that's how it's going to be, eh?
So the skis are tuned similarly, and the bindings are mounted "as recommended" on the manufacturer-indicated lines. That may
eliminate my first two concerns.
But it may not, too. I'll take your word that the tunes are the same. But I have very little faith in manufacturer-suggested binding mount points. I am fortunate that the VIST Speedlock bindings and plates I prefer allow substantial fore-aft adjustment over several centimeters, which allows me to experiment until I find where my skis work best (for me). Rarely (not never) is it "on the mark"--typically, it is one or two centimeters forward, sometimes more. Virtually never is it back.
I find that it makes a surprising amount of difference in how the ski skis. Since I often switch bindings from one ski to another (they clip on and off with the flip of a lever), sometimes I can't remember which position I prefer for a given ski. But I can tell in the first turn or two if I've mounted it wrong, and a quick fix brings the skis back to the way I like them. (Yes, I know, I could put a mark on the ski and eliminate the problem. But that would be too easy....)
Anyway, no telling if binding mount location is the problem on your Elans or not. It seems unlikely, actually, but if the bindings are in the wrong place it will make it awkward for you to stand easily in "neutral" over the sweet spot. It will require effort, whether you're aware of it or not.
For that matter, it could also simply be different bindings themselves, if they involve different "delta angles" (the difference in height between the toe and heel platforms, which affects the fore-aft tilt of your boots and, therefore, lower legs). If the delta angle is not optimal for you on the Elans, it will again require you to move somewhat less naturally to maintain fore-aft balance and to control fore-aft pressure.
Still, it seems more likely that you're just experiencing a difference between the ski designs themselves. Some skis do feel like they have a huge sweet spot, with a lot of communication that tells you when you're "in" or "out," and even a tendency to feel like they want to pull you back to "center" naturally. Others don't.
From your description of the symptoms, though ("hooky, squirrely..."), it still sounds more like a tune issue on the Elans--like they may be concave or railed, or have too little base edge bevel. I'm sure you trust your hand tunes, and your "Montana" shop for the flat grind. But have you actually put a flat bar on them to confirm? (For what it's worth, there are very few shops that I trust--and none that I would trust enough not to check their work with a flat bar....)
Of course, you could just ski on the Fischers!