Dave,
Nice legs......
I think that the best way to secure the basket would be to epoxy 4 pieces of plastic (about 1/2" thick) to the bottom of the toilet tank, just inside or outside of the basket perimeter (or both). Then, I would screw clips into those plastic pieces. I'd suggest making the pieces out of something round so that pieces of waste don't get trapped in corners.
Check to find out what kind of plastic the tank is made of. I believe that epoxy would work well on it. Definitely do not use any urethane or silicone based sealer or glues. If it is made of PVC, use PVC glue. That will
weld the pieces in place. If it is made out of polyethylene, it cannot be glued.....don't even bother trying. You would have to take it somewhere that has a plastic welder. Make your pieces out of polyethylene and have them weld them in place with polyethylene welding rod.
Actually, I think that basket design "Stinks". I think that I would have designed the system to partition off the pump. The same screen method could be used but I would have molded in a slot for a flat screen to side down from the top and partition off the back 3" of the tank where the pump is. Having that basket sitting loose in there seems like a recipe for having solid waste trapped on the wrong side of the basket and not being evacuated when the system is dumped.
As for a trap door, you can get spring loaded doors at Home Depot. They make them for microwave oven exhaust fans and all sorts of other things.. I may try this the next time that I install a new microwave oven in one of my apts. I usually throw away that vent panel that comes with it. The thing to remember about putting a spring loaded door on there is that it can only seal tight enough to keep waste from splashing out when towing. If you make it air tight (Or even close) you will have to vent the toilet some other way.
If you really want to add a holding tank, you may want to consider having one built. If you can find a steel fabricator, it would be easy to cut pieces of steel the exact size required for a top, bottom and whatever sides that you need to close in that area in your frame, making it a sealed tank. It's just a matter of designing what you want and coming up with the fittings need to attach to the tank. BTW....you could have the tank extend a few inches below the frame and probably increase the capacity to about 8 gallons. I would suggest having a 12" opening port in the bottom of the tank. That would allow you to have access for sealing the steel before using the tank also for cleaning and servicing.
They do that on steel boats all the time. The steel hull and framework make up the bottom and sides of the tank. They just close it in by welding on additional plates. It's strong,
relatively light (because you would use part of your existing frame as part of the tank) and it is easily sealed. It would also be strong enough to endure tire blow-out damage.
Myself, I'm quite happy with our toilet. It gave the prior owner no grief (for 10 years) and it has serviced us well for the last 6 camp-outs.
Wayne