Few things I would try, more tire pressure helps tire shake in some cases, you dont have a lot of hp so its a combo issues not likely the tires but you'll need to go upwards of 6-6.5 just to see what it does.
What rpm are you doing your burnouts at ?
I think a different gear would help get rid of some wheel speed and help your issues. Conv also is to tight for the combo which is not helping things. Need something around 6000