You should have the Quarry output into an inventory(like a chest) first and then extract items from that chest. The problem you are having is with momentary spikes in item output and pipe/duct throughput limitations. Having the inventory there as a buffer will help smooth things out.
Ideal would ofc be to use something like an Ender Chest so that you do not have to move all the extraction from the chest every time you move the quarry.