You will get lift at those speeds and you need to realize that a chin spoiler will help BUT what you are describing is also a cross wind scenario.
Put in double adjustable shocks and lower the car as much as you practically can in the front. The new springs and shocks will be stiffer then the stock ones ever were and will probably reduce the suspension travel up and down somewhat which will help reduce the bump steer you probably are experiencing as well?
IF you are still running the stock shocks most likely the 1" spacer doughnuts are still on them.
Removing them absolutely will help some. If you do. Measure the ground clearance that you do have now under the radiator support. That's as low as you dare to go and you might even want to consider mounting a skid plate there as well so you don't get "hooked" on something.
Then go back and check that you have sufficient toe in both front and rear. 3/16" to 1/4" total is a good number to aim for.
IF you intend to drive the car more at those speeds then you had better do a "bump steer" change check. It's possible that the pulling to one side or the other suddenly is "bump steer" caused by a sudden toe out in the suspension travel at one point.
That could work out since you will be removing the springs and shocks for new ones and you need to do that to check the bump steer changes. You HAVE to know that to understand what you are dealing with.
Also be aware that at that speed the aerodynamics could push the car down or up. When you get lift in the front it isn't smooth. It's sudden and it's a little like a speedboat's nose bouncing on the water AND the car can steer itself left or right like bump steer would. You don't want to be chasing the wrong solution.
You can only calm the car down so much, then you either have to live with it or decide that the car has a speed limit...or you do. It's not a simple solution there to anything.
The encouraging thing is that the basic design is quite capable of running over 170 or more with relatively simple "improvements" to the production settings. How high is up is difficult to say but I personally would be staying away from envisioning anything near 200mph. The car MIGHT be capable of it but I am not. That is professional racer territory and you just can't go out causally and expect to do it.