1998 Dodge Neon Violent Shaking Taking off in 1st gear

I rode in a modified srt4 once. When the guy would take off the dash would shake violently from the tires failing to grip, until finally they would, and then the ride was smooth and fast as hell.
I own a 98 R/T neon that has been modified. One modification included a performance flywheel and clutch from clutch masters. Everything has been great for about two years and I rarely dog the car. Out of nowhere, it is starting to shake like that srt4, taking off in normal driving fashion, but only in 1st. The catch is I'm not upping the rpm before I let off the clutch, so it shouldn't be peeling out so violently. I have searched the internet and can find nothing of this nature. I'm totally baffled. You guys ever heard something like this?
By the way there is noticeable vibration in the clutch peddle after depressing it past the first inch of play. Also, the rough shaking is definitely worse when trying to go uphill, in 1st gear, from a dead stop. Feels like you're pealing out, especially if you let up off the clutch too fast, giving it little to no gas. It feels like the car is pealing out on its own, but there is no burnt rubber or anything.

Thanks for your help.
-ORGNL RT-