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(end of rant)
In theory it can be done but the deeper you dig, the more complex it becomes.
If you want to do it for the sake of doing it then you can go for it but it's really one of those projects that are too complex to be worth it in normal cases.
It's possible but very ugly.
The way I would do it is to set the inserter whitelist based on the contents of the chest or, if the chest is empty, a random item from the belt in front of the inserter.
Then you take the contents of the chest, set its value to -100 and add it to what is on the belt in front of all subsequent inserters to only add items which have not already been picked up to the whitelist.
https://steamcommunity.com/sharedfiles/filedetails/?id=2792592300
You can only have 5 whitelisted/blacklisted items for filter inserters and 1 for stack filter inserters so this isn't going to work.
Have some constant combinators with signals for each of the potential goods arriving on your sushi belt. Set the values to one. Also, you need a few combinators for each chest:
1. A combinator (let's call it A1, A2, ...) which has output values of the chest content of all chests before as seperate signals. (For examply something like "* + 0 = *", with inputs from its own chest as well the output of the combinator of the chest before)
2. A second combinator B1, B2,... which multiplies all inputs from A with -1.
3. A combinator C1, C2, ... which checks if its chest n is empty. Use also the values of Bn and the constant combinators as input. If the chest n is empty, send the input values to the inserter to set its filter. The filter will then not be set to any item already stored in the chests 1 to n-1.
4. Additionally, connect each inserter with its box to set the filter. If anything is in the box, the inserter will be set to the good in the box.
I hope you get the general idea. I haven't tried it out and it might have a few problems, but you might use that as starting point. It might also lead to situations in which the whole system could get blocked.
Ty for the help though!
Also, Storage Chests and Buffer Chests have a higher priority than Passive Provider Chests. This means that if you request 100 Red Belts, and have 100 each in a Passive Provider and a Storage Chest, the Storage Chest will be emptied before the Passive Provider gets drawn upon.