Joel,
You can get Mc Creary in a dirt (must be dirt compoud for outright grip) compound that will do the job very well. They are not considered as highly as the MT's but are basically the same construction -IE they are intended for drag work, soft side wall. Cost is well in the region of your budget.
The shop is called Mc Noughton tyres - I have posted their details before.
Call me if you want further info on their suitability.