Do not get ahead of yourself.
Swapping the original modules and not seeing the problem swap sides is indicative of the modules NOT being the problem.
Seeing the problem disappear with the new modules only means that you have removed the problem but Not that you have identified the problem.
You have not identified the problem until you can Re-create the problem.
You have previously demonstrated that Either Original Module will operate correctly in the "B" Position and...
Neither Original Module will operate correctly in the "A"
Swap your old modules back into the engine one at a time into Both the "A" and "B" positions to identify which module has the problem.
If Both work in the "B" position and Neither Still work in the "A" position, the problem is the Position and NOT the Modules.
If neither module re-creates the problem, then you have probably fixed some other problem during the swap.
The number one suspect would be the wiring harness in general and the connectors themselves in particular.
The old troublesome connector on the harness may just be making better contact with the connector on the new module.
Have a close look at the connectors, and then have a closer look with a 10x magnifier.
A firm tug on the individual wires may also reveal something.
Until you can re-install the bad module and see the problem reoccur and follow the module, you can not say for certain that the problem was a module.