My experience is tire shake is caused by not enough power or too much traction . With our Heritage jrfuler, when we have tire shake we lower the tire pressure, will usually run around 6 # but as low as 5 1/2 # . By lowering the pressure it cups in the center so the edges are doing more of the traction . You can check that by using your temp gun after a run at the turn-off and measure the temps all across the tire, and you'll see higher temps on the outer edges.
Or you could just up the power by adding more nitro % , or go to a smaller tire JrFuel A cars run about 1100-1200 hp and 6.80's to 6.70's and run either 31x12x15 [ GY]or 33x12x15 [ M&H], and run as low as 4 3/4 # Another example is the Heritage A/F guys have found going to the N/TF M/T Bubba tire[ 33x12x16, stiff sidewall] has solved their tire shake going away from 33x14x15 GY.
I think since the tracks are preping with more VHT = more traction=more tire shake , it's harder to keep the tire speed up so it does not pull the motor down out of it's power range.
You could try more rear gear and or 1.80 1'st gear. I think only super comp want too much traction with their delay boxes.
I'm running the latest batch of GY 31x12x15 thru Hayden wheels, and 33x12x15 MH on bad tracks and will try 30.5x10.5 [ 11 1/2] x15 MH next.
Good Luck , let us know what works for you.
Jon