i don't think the problem is in the sway bars - adding stiffer mounts, or drop links will only exacerbate the problem - only if you had sway bar binding would this be the problem, and i don't think you have that going on
i think you need to go the other way on the shocks, and set them either at full soft, or just 1/2 turn from it - this is due to the stock spring rate of the torsion bars - if you had stiffer torsion bars, or additional helper springs, then you could increase the shock rebound rate
as for the front springs, that is pretty easy to figure out, if you have the ability to measure the wire diameter, the coil diameter, the free length and the number of coils - also, if they are factory springs, they would have dots on them, and i could decode that for you
as a distant possibility, and i seriously think you need to soften the rear shocks first, but too much rear camber can lead to this snap reaction too - as the car rolls over onto the outside edge of the outside tire, and releases the load on the inside tire, which then extends, and when the weight starts to come back on the inside tire, the outside tire extends with a bounce - we have all bounced a tire on the ground - what we often fail to remember is that the tire itself has a built in "spring rate" of sorts, and it can be bouncing the car around in a corner - with a lot of negative camber, this forces premature loading of the outside tire, and forces it to compress and then release - this can be with a LOT of force under the wrong conditions - to correct this, try increasing rear tire pressure a bit - this will resist compression more, and decrease the pressure differential under compression - i know it sounds backwards, but it works - i know the rule is to decrease pressure to correct oversteer, but that is for loaded oversteer, and not rebound oversteer, like what you are describing - there are 4 kinds of oversteer (loaded oversteer, as in a constant turn, snap oversteer, which is what happens when spring and shock rates are wrong, compression oversteer, which is what happens when a tire rebounds, and power oversteer, which is what happens when you lose traction under power in a turn), and each one gets a different kind of corrective measure
try softening the shocks first - that is easy, quick, costs nothing, and will tell you right away if it's the problem
and send me info on your springs