Add a second axle. if for no other reason just to make for a more balanced trailer thats not going to rock around with people on it. As for stiffing it up... I bet if you put a wood deck on it it will be more then up for your use.
That's exactly what I'd do. Axles are not too expensive. I'd get 3/4" (Minimum) Marine plywood for the deck and secure with HEAVY bolts every couple of feet AND secure these bolts with LARGE, HEAVY washers top & bottom.So in your opinion the frame wouldn’t need to be modified at all? I know some people end up adding angle iron to reinforce it. Just build a solid wood deck and add a second axle?