It seems that mathematics is a "god of the gaps".

"...gaps...due to not including (or not knowing) important mathematical conditions"

So maths is a "god of the gaps"; you are assuming that one day some maths will turn up to fill the gaps in current understanding!

Regarding electrons: Roger Penrose has considered the possibility that in the universe there is only ONE electron, one proton, one neutron, etc.

Michio Kaku's "Hyperspace" shows how this can work: in higher dimension space; you may have one electron; in lower dimension space, you have numerous views of that one electron. This way, the incomplete-view of "electron" from lower-D space gives many "electrons". A difference of any sort is still a difference.

Conservation laws make no difference; they merely provide evidence of the "one electron in hyperspace theory". In lower-D space, a difference in location, in fact any difference that lets you put an "s" after the word "electron", is sufficient for you to count them. If you count more than one, it is logically impossible for you to not have difference between them FROM THAT VIEWPOINT (eg, from the point of view of "location").

Different location is plenty of difference. It doesn't prevent those different locations from being different views of a single, universal, hyperspace electron.