How to transfer object from one list to another while comparing the two

The challenge is this: I need to figure out a method to transfer one item at a time from one table to another, loosely based on this approach:

This was easy enough at the beginning of the project when the tables were simple. Here are the updated requirements as the product is beginning to mature and the user's needs are better understood.

The new tables have much more content and we are targeting 1280px width machines. Here's a realistic representation of the content. Users need to be able to easily access both tables for comparative purposes (what's already in the inventory vs what I'd like to add) The last step will be to commit the updates

It seems like a stacked approach presents some usability issues of having to scroll the screen up and down a lot and keeping several items in memory, making it cognitively taxing. I'd really like to try and avoid a horizontal scroll and am open to rethinking this approach entirely.

Also, the search will most likely be fairly broad so we need to allow for many possible results.

Any ideas would be greatly appreciated. Are there any existing examples of solving this problem that anybody can share?