They can't carry it, but they can get you there first and let you get started digging it. I remember some of these games where it turns into a slugfest at the Prize when both sides have infantry get there around the same time and everyone's hacking away to get to the one model trying to dig that turn. Rather than getting into such an attrition of digger/carrier models in the center, get there first and try to get away before anyone else arrives.
I think the thought above is to use the Cavalry to get there fast, maybe a turn or two ahead of the enemy. Most of the cavalry can then keep going past the objective to engage and delay the enemy force while one or two models stay behind to start digging. One of these should be a Hero since you can use Might to adjust the roll for recovering and it's critical you get moving first.
So Suladan drops from his horse and digs, while the rest of the riders run interception. The Easterlings and Haradrhim are rushing forward to guard his retreat while Harad bowmen are volley / direct fire prime enemy targets from a flank side. When Suladan (highest armor, great combat abilities, M/W/F to survive, big stupid sail to help him go faster with the wind) has the prize he starts rushing back for his board edge, hopefully passing thru the tough Easterling line and leaving any pursuing models to try to penetrate that. It really needs to be only a short delay.
I believe you can also set up a bucket-brigade. Leave a chain of models just under a full move apart from each other starting at your deploy zone. When you recover the prize, rush it to the nearest model in the chain. They then do a move to the next model and pass it on. They then move to the next and pass it, etc. all the way to the edge. If set up right (and you're not risking Courage tests for broken
) I think this will let you get the prize off the table in one turn after recovery in best-case. I'd strongly suggest double checking the rules about carrying and passing something before you try this though.