Solution: Get a modern car but simply build a Faraday cage around it, like those anti-drone "cope cages" you see on Russian tanks.
cope cages look like hardware fence (like chicken wire but welded, pig fence, sheep fence, goat fence are closer.)
However, the US already put fencing around fighting vehicles, specifically the Bradley, where the fence was essentially "chain link fencing".
I'm not entirely sure i buy that the cope cage stops drones; but the chain link fence absolutely stops RPGs from exploding by severing the wire that runs on the outside from the tip to the explosive.
I believe faraday cages need to be grounded. I'm not sure what the resistivity of rolling rubber tires are.