That's your starting Point: compare the variants of those functions that you want to centralize by your module to find out how you should parametrize them. Then, instead of copying and modifying, set a good example by copying and creating a module (and, of course, eventually using that).

This will take more time, so you might have to do it alongside, but once it is usable, you can use it to convince your colleagues (I don't think your management mandates copy-paste-programming) to take this road.

Of course, further adaptations/modifications of the new "central" module can break those scripts that already rely on it, so it's important to include at least rudimentary tests, lest it will be turned into an argument against modularization…