I think the CCA of a battery is just about absolute maximum that can be sustained for 5-10 seconds, and is about 5 to 10 times the nominal A-H rating. So a 90 A-H battery might have a CCA rating of 600 amps, but that should be only for occasional use. Generally about 1/2 the A-H rating is about the maximum you want to sustain for any period of time, so figure 45 amps. And even that may only last about an hour. You can get close to the full A-H capacity at about 1/10 C, so maybe 9 amps for 10 hours. Lithium and NiMH can do better.
It seems that the "Green Dawg" or "Rock Dawg" uses just a 10HP electric motor which can give short bursts up to 40HP for 5 seconds, so for that you would need 30kW for 5/3600 hr or 167 W-h. You can get an honest 50 A-h and 600 W-h from a single battery, but you must figure the peak power. 30kW is 2500 amps. But you don't really need that much HP if you are going slow, so you might need to start with the total torque you need. You want to be able to essentially climb a vertical wall so you need a total force equal to the weight of the crawler and passenger. Let's say 1000 pounds. With 24" tires that is 1000 lb-ft. 60 RPM will give you a speed of about (24*3)/5280 miles/minute or 0.8 MPH. The power needed is 1000*60/5252 = 11.4 HP. Half that on a 100% slope (45 degrees).
So if you can be satisfied with about 1 MPH on a 100% slope then a 5 HP motor will do. That's about 3.8 kW and you want to limit battery current to about 100 amps, so you need 38 volts, or three batteries in series. If your non-climbing travel is fairly level, and no more than 10-15 MPH, you can probably do that using an average of 2-3 HP. Worst case, the batteries should give you 1800 W-H which is enough for about an hour, or 10-15 miles before charging, except for what you use when climbing.
It may be a good idea to use hydraulic motors in all four wheels, as the "Green Dawg" seems to have. That will give you 4WD without CV joints or U-joints. You might be able to scrounge some hydraulic stuff from garden tractors. Hydraulic drive gives you very precise control and excellent hill-holding ability.
Just some ideas, but I think you could put something together for under $2000 if you can do the work and get parts from a junkyard. You might be able to use a three-phase motor and a VF control, and power it from a 3000W 240V inverter, although you'd probably need to wire the batteries in parallel to get 12VDC at 250A. Otherwise, you can use twenty smaller batteries to get 240 VDC at 15A, or 30 batteries to get 360 VDC at 10A.
Good luck! Seems like a pretty cool sport.