Yeah, fat skis are fine off piste. The marketing lie is that fat skis perform well on groomers. Again, going back to what the OP wants, he said he was concerned a fat ski wouldn't perform well on piste. And given what he's used to, a fat ski will not perform well, or to even close to the same degree as a narrow waisted ski, on piste--unless he's actually just skittering down the mountain (and I'd like to give him much more credit than that).
For me, I feel effective technique on a modern, narrow waisted ski negates any "training wheels" effect of a fat ski off-piste, and I still get to enjoy carving sensations on the cattracks back to the lift. And I enjoy the focus it takes to manage pressure underfoot in 3D snow. It's a different sensation from what you get on a fat ski.
Honestly, if the focus is on making things as easy as possible, I'd suggest most folks would be happier with a snowmobile.
Anyway, I assume the OP now has enough info to move forward.