I realise it is counter-intuitive, nonetheless when the grip comes up you need the car to be softer. Additionally, the car needs to have smaller diameter tyres to remove some sidewall flex. Try 45mm fronts and 47mm rears.
You can also brush superglue on to the sidewalls of the front tyres to remove some grip, but that should only be in extremely high grip. The glue should be sidewall only, to the top of the sidewall, but not any on the tread of the tyre.
I see lots of cars where drivers are going harder and harder on the springs and tyres as the grip comes up, and then having grip-roll. The reason that it works better if you put some additive on is because that softens the tyre. As a rule of thumb, as the grip comes up use softer fronts. If the level of grip locks the rear in, then go to a harder rear.
50 front is too hard for your carpet. Go down to a 45 and see what happens, if necessary go to a 42. IF you can true them down to 47/45 then do so.
I do think from your description there is something up with the car, so a rebuild with the instructions in front of you might not go amiss. I've been doing this for 35 years, and mistakes made when building the car are still in my repertoire! HTH
