Bioactive is 100% doable with a screen cage, though I found I ended up needing to make more modifications to my ReptiBreeze build than I did my ExoTerra.
I highly recommend that you either find a planter box with the right dimensions for your cage to sit on, or make one. While you could, theoretically, use some sort of heavy plastic liner to fashion a "planter" in your cage, it would be near impossible to move, take up ~10+ inches of real estate off the bottom, and (imho), look ugly.
Here's the simple planter box my grandpa made for Lily. I sealed the outside with 2 in 1 Varathane/stain, and the inside with several coats of LiquidRubber (similar to FlexSeal). Even with the sealant, I chose to line the inside with plastic before building my substrate layers to ensure that there isn't any seepage.
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Since screen cages are a little wishy washy, I'd recommend either Dragon Ledges or some sort of frame to easily attach any sticks and pots to. Saved me a lot of grief, and also protects the screen from damage.
You'll likely need more than just springtails to establish a strong ecosystem. I'd recommend at least getting some isopods, and I personally also run red wiggler compost worms and some detritus milipedes that came in with some leaflitter. Should you get isopods, they benefit from cuttlebone (the stuff you give to birds) as a calcium source, and like some bits of cork or bark to hide under in addition to leaflitter. I'd also recommend some sort of commercial CuC food at least while the population is getting established. I use Repashy Morning Wood, personally, and still end up feeding once or twice a week to keep up with demand.
If you prepare things properly, you won't have to move your cham out of his cage for a long period of time. Make sure any assembled elements that need offgassing (planter box, background if you do it yourself, etc.) have at least a week to air out (or until they stop smelling; follow manufacturer instructions). Pending whether or not you have a spare cage/lighting, you can put your boy there for a couple weeks while the enclosure is settling... but I personally didn't bother. Once you have your supplies and your cage is ready for assembly, you can just take your cham and put him in a box overnight, let him wake up in his new environment the next day. Imo, this would be the least stressful.
I ended up using a combination of ProMix HP High Porosity (equivalent to SunShine Mix #4), orchid mix, worm castings, and a little of this and that that I had in my gardening supplies. I can't remember what I've posting where and to whom anymore, so here's a breakdown of my layers and drainage system:
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PVC drainage access pipe.
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Let me know if you have any additional questions. I'm barely awake, and probably missed something!