I understand now - the lower channel is below the level of the reservoir, so can't drain back. That is obvious now that I go back and look at your photos.
I like the run-to-waste-idea. Wonder where I saw that? Ah yes, post #15
But seriously, you've got a few options:
Put a pump in the lower channel feeding the top back into the reservoir and maintained by the float valve. This is already working for you to an extent - you just have to add the pump - and you have already pointed out a couple of potential issues. It's a bit complicated, and the only thing I could add is the risk of the float valve becoming stuck open because you are running SIP and there is a lot of crap in your water (soilless media being pushed out the bottom of the pots by the roots/being washed into the channel by the water motion etc), so if a bit of dirt or something jams the valve open, you could flood your tent and eventually run both channels dry.
Air stones are a good idea: this just turns the lower channel into a shallow water culture set-up. Because the water isn't really being recirculated, you just have to make a bit more effort to change it out regularly (like, about every week or so).
Another option would be to raise the tent - get an old table and cut legs down (or something like that) - and have an external reservoir that is lower than the bottom channel (under the table) and pump to the top channel, then waterfall down to the bottom channel and back into the res. I don't know how feasible that is for you, so it's just an idea . . .
The last option is run-to-waste. Replace your air pots with normal pots. Fill them with pure coco. Put two or more spikes into each pot (always have more than one line going to each pot for redundancy, and in case one line gets blocked for whatever reason) fed by 4mm flexible irrigation line coming off a 1/2" main line fed by the reservoir pump. Put the pump on a timer - one minute, four times each 12-hour lights-on period (no flow during lights off). You will need a tap/valve to regulate the pump flow to the bottom channel, otherwise it will get most of the flow (gravity obviously acts against top flow). You'll work it out
For drainage, you can get a length of any old 1/2"-3/4" garden hose and run it to a house drain, or outside, or into a shallow collector. Run-to-waste would be the bomb in your set-up, as you wouldn't have to change a thing (just add feed and drainage lines) and you will waste less nutrient solution than you do now. With RTW, you run your nutrient solution at a reduced rate (if your nutrients run 5ml per litre in a recirculating system, you run 3ml per litre in RTW etc), and you limit your runoff to around 10% of what goes in. In your current set-up, that reservoir would last about two weeks or so - which is the same as replacing it every two weeks (except with less nutrient going in).
No-one likes the idea of RTW when they first hear it, but the reality is it's a very efficient system. You can even recycle your waste runoff by using it to water your veg or flower garden outside. I have run lots of different systems over the years, from DWC, to NFT, to RTW, and run-to-waste was the easiest and most reliable.