[strat61caster]

1. Shot in the dark but Hankook RS-4 would be my guess, size will be preference, buy what's cheaper and focus on seat time, use the Nittos for awhile longer, low grip teaches you good things. There are a few other 200TW tires that could fulfill the same purpose. Give up a run and have an instructor drive your car with you sitting shotgun, I learned a lot more doing that than any passenger shouting any advice at me possibly could teach. Videos are useful for comparison too.
2. Toe in may help, take it to a different shop if they're saying you're maxed, you don't need toe arms and the Whitelines should be able to get you over -2.5 in the rear with stock toe arms. Every nationally competitive 86 STX car has stock toe arms, I've heard as much as 1/2" and run as much as 1/4" but that's a work in progress on my end.
3. Just try detaching it first, see what happens, no cost tuning, can probably do it in between runs.

A good driver can make any car feel ok, a bad driver can make the best car in the world feel like crap, don't start throwing money at the car when the nut behind the wheel can have the biggest effect. You may be unsettling the car and creating problems not related to the way it's set up. Damper adjustments also may be playing a part in what you're feeling as well, maybe softening the rear will get you what you want.