Disclaimer: I'm making this suggestion prior to the launch of update 3. One of their teasers did seem to feature some sort of machine that consumes assorted parts. If that machine works in the same vein as what I'm about to suggest, then obviously ignore the suggestion.
Now then a couple things to note: First, I've seen a few people suggest on occasion the concept of a disposal unit. Basically a means of automatically throwing out excess production.
Second, the space elevator, for all its glory, seems to be fairly under utilized. You use it a handful of times to unlock tiers and it's generally easier to fill it by hand than bother with the conveyor inputs.
Use the space elevator as a "disposal" unit. Allow players to build logistics to direct materials into the elevator. This would also give the opportunity to launch it more frequently as well as give players more of a reason to use those conveyor inputs.
The player could be given achievements for sending set amounts of a material. It would be a more productive and incentive-based style of play as "Oh, the container filled up again... let me just throw everything in the trash since I'm not using the stuff."