After some amount of pain with sushi belts, I've just stolen the design from Nilaus with passthrough filtering splitters and bots, so very much similar to your setup but two main belts.

https://youtu.be/qr_Lep5UCJU?t=37m2s

Not at pc so don't have a BP but basically like this:

The outter belt is the overflow that goes through an array of speed boosted recyclers and the output goes back to the inner main as priority input.
You do have to account for the secondary outputs of the recycled overflow, so green circs, iron and copper plates, iron ore etc

Edit: the item filter of the storage chests must match the filter of the respective splitters (obviously), like this bots will prioritize these chests for both requests and "storage". Edit2: it is ready for quality upcycling but we didn't have time/felt like it at the moment