TL;DR
Add priority numbers to logistics chests that tell logistics bots to prioritize one chest over another.What ?
Add a text field to all logistics chests where the player can input a priority number.When fulfilling a request logistics robots will prefer a higher priority number over a lower one within the same chest type.
Why ?
This fulfills the same need as priority splitters do for belt transportation.Since belts also provide a buffer they are not suited for all types of transportation. (e.g. high value low quantity items)
This makes using splitters for priority unsuitable in many situations.
Example:
You are producing item A.
Item A is used in process X and Y, but can also be used to make useful item B.
You want item A to be provided with the following priority: process X > process Y > item B production.
This can be achieved with belts using priority splitters, but not with robots.