You are likely overthinking this quite a bit. Assuming you can find 2 blocks of foam big enough (or one that's too large that you can cut down to the right size), you can just shove foam (it should be snug but not too tight that you have to use force to get it in place) into both chambers. Then use a water pump normally in the third chamber.Oh, no it didn't have that.
That's the flow pump in the bottom image?
If I got a replacement water pump, and capable air pump, how would you feel about the following setup?
Orrrrr, I might go with the submerged pump and block of foam idea. I think they'd serve the same purpose.
I just had a few air-driven sponge filters laying around already.
Thank you for the pump link, @DaveKS!
I would ditch the air pump altogether unless this is going into a fish room. The reason being that they are noisy. Even if the air pump itself is near silent the sound of the bubbles in the tank will be noisy. It's also not needed unless you are overstocking this tank to the max. Planted tanks with light to moderate fishload are the way to go and it sounds like that is where you are headed anyway.
If you find yourself wanting to polish the water more you could make your second piece of foam be less coarse, but likely it won't matter if you go with a medium grain of foam for both slots. Just stuff them full and you will be fine.