When you say first chamber, are you talking about that first picture of the overflow area? Or the first layer in the three layer rack in the main chamber?I just don't know the ratio of what is a good amount of cheato to how many gallons of water and livestock to actually make an impact that a person would find it not working, sub par, or the greatest thing since sliced bread. I think you might find it in the sub par area, but it is one of those things you never know till you try it kind of things. Maybe there is something online for the sum of cheato to water/livestock ratio.
Otherwise I would say just do filter floss(pillow stuffing roll not sprayed down with chemicals that you can find at a Michaels craft store. Cut to size and placed in that first chamber. Replace every 3 days if you have GHA(green hair algae). Bag of Purigen in the second chamber. Bag(s) of MP spheres at the bottom. That way the only thing you have to replace is the floss when gunked up and Purigen every 6 months or when exhausted.
Ill wait on implementing the Chaeto depending on my tanks stability and parameters later down the road. If I'm not seeing any issues, then I see nothing wrong with keeping it as simple as possible and removing an un-simple task. I've always loved using the KISS method whenever applicable [emoji6] [emoji106]