Do you have a picture of what your work in progress is going to look like? Judging from just the written details, there is so much wrong with this idea. Ideally, should be mounting the entirety of the 4-slot in the orientation you'd like to have your cartridges inserted.
The best option is to make a case that doesn't require the cart slots to be rewired. I don't think you quite understand the pain and suffering you're trying to fling yourself into, on top of having to face the reality of strange unexplainable issues once you're done soldering.