You could use the factory jack and use this with it.
AEV JL Wrangler / Gladiator Spare Tire Jack Base Booster https://www.amazon.com/dp/B08HSM5Y7P/ref=cm_sw_r_cp_api_i_FDNEFSQVFJJ2EP4CPPX4
Since it’s from amazon if you’re not happy with it you could return within 30 days of purchase and go another route.
You an buy this from AEV. It stores by strapping itself to the firewall in front of the passenger floorboard. Pretty cool. Also, a 37 will fit in the spare tire location just fine. I do it with mine. I did have to remove the heat shield, but I read that you don’t have to with some tires.