What I want to be added is a menu added to the Inventory Connector, or a new block, that allows the player to set what block's inventory should be filled first.

For example when used in conjunction with the Create and Extended Drawers mods with a setup like this (see image):

There should be an option to prioritize the drawers since they show the item count.

A block would probably be the best way to get this done since you can have a new block that goes in between 2 pipes and will make that pipe prioritized for items to be put into.

Edit:
Or just have it so that the chests that appear first in the pipeline would be filled first (see image below):

Filtered cable connectors have a priority option, just leave the deny list empty.