I would cut a bit of 10mm or 12mm plywood to fit underneath of the main frame section and use cable ties to hold it onto the frame. Probably at the level of that bar across the back of the trailer. That gives you a lip around the platform as well as a very slightly lower centre of gravity. Having lots of cut-outs where things are attached to the button of the frame isn't too much of a problem.
Ideally you'd find a plastic bin that exactly fit into the space but that's very unlikely to be possible. You will most likely find that the bin you get either sits too low and scrapes on the ground, or is too small on one side to work properly. If you go this route I suggest getting one the right width to sit on the main frame members and not worrying too much about how long it is. Having two bins next to each other might also work.
I think keeping the cloth cover will be handy, it will help keep your load in place as well as giving you some shelter from light rain.
Be aware that kiddy trailer load ratings are not the same as cargo trailer load ratings. No-one is expected to add exactly the load rating of children (look, it holds 2.3 children!), and people tend to be more gentle with children than with cargo. So a 30kg cargo trailer will probably hold the same weight as a 50kg rated kiddie trailer before it starts falling apart.
The reason they cost so much is that people won't buy a cheap, heavy, solid trailer. Instead they buy cheap, light, flimsy trailers and wonder why they fall apart. I built 12 of the heavy style and it took more than a year to sell them even though they cost the same as the flimsy junk ones. That as an educational experience for me.