Another option is the worm gear axles from a losi mini crawler. Won't have the native gear reduction the tamiyas would, but they are v strong and wont break. Perhaps you could even hook them together.. IDK.
Tamiya also makes a worm gear box like the one posted above.
I think Linc is right on making it FWD. May help with the pulling as well. RWD would likely just backflip. A crawler type veh seems best suited for this challenge
The rules he posted says it has to be either RWD or 4WD.
Are the batteries going to be alkaline or NiMH?
No fun. I guess rwd will be easier to make the 4wd... With just 1 motor that is. Or use the tamiya worm box and split it off to 2 live axles with 1/4 elliptical springs for location. You can use the high lift springs and cut them in half. I can't imagine you want this to weigh much...