Faster Way To Move Items?

I'm playing Project Ozone Kappa mode and just found out this interaction

If you have Item Translocators and Thermal Expansion, you can use translocators instead of servos to input items into a pipe system almost instantly with the benefits of having advanced filters, like so...

I would recommend using the item conduit from EnderIO mod, it is a lot more faster than extra utility's transfer node and much more efficient. You can stack cables on top of another up to 5 cables in one block, that means with item conduits, they can share the same pathways together without having to find another path that doesn't intersect or cross with each other. This makes it much less redundant in comparison to the other transport pipes.

Just the item conduit itself, wold be fast enough to handle deep storage unit. Additionally, if this is too slow for you there are stack-able speed upgrades that you can put on, the speed upgrades are relatively cheap. I've never needed to use a speed upgrade on a Ender conduit before, but this option seems to fullfill all your provided criteria.