No reason you should not pay fuel tax on your propane fueled rig. It tears up the roads as much as any gasoline or diesel powered rig, so it is a fair tax.
We have run a couple of propane powered heavy pickups for many years.
Our state (ND) allows you to estimate (MPG VS miles per year) to come up with the gallons of LP used on road per year and pay the road tax on that amount. Bulk propane price plus road tax is still a bunch cheaper than $4 per gallon gasoline.