Oboe- please allow me to add a coupe of thoughts about your situation.
Do you know how a ski with a firmer forebody than tail is supposed to react?
It generally will require greater forward leverage to initiate the turn. But since we don't want to be moving fore and aft as much as we did on straight skis, the shovel is made wider to compensate. With the softer tail, as pressure builds during the second half of the turn, if it is not managed appropriately, the ski will bend into an increasingly tighter arc, shortening the radius, causing a greater trend to end up in the back seat.
The reason a few skis are built to these specs is that faster off piste skiers rely on the ski not to turn too quickly at the initiation of a turn, but like to have the ability to cut off(finish) the turn, if necessary.
One of the earlier versions of this theory that I can remember was the Hart Honeycomb Cruiser(circa 1977-78). It ripped in the thicker Sierra cement, was incredibly stable at speed, yet would turn on the proverbial dime if given the correct inputs.
With these thoughts in mind, some gentle modification to the inputs you give the ski, combined with an understanding of it's tendencies might give you the answer you have been looking for.
But at the risk of drawing your ire, let me also suggest that today, every ski on the market has a very unique personality. You have a specific skiing personality. The challenge confronting each of us these days is to find the match between our personality and the ski's. When you do, it will be magic. You think, the ski does. So don't get too locked into a specific ski.