If anyone is offering a definition that is a synonym for “notwithstanding”, then just use “notwithstanding”.
“Modulo” has a distinct usefulness that is to do with remainders (i.e. what is left over after you put items into groups), and contrary to many other opinions here, it is useful beyond mathematics.
Politicians vote along party lines, modulo party membership
means
Politicians vote along party lines, split into parties and as groups, with a few leftover (sometimes) because they don’t fit into parties
and not simply
Politicians vote along party lines, unless they don’t have a party
along with the missing implication that most have them always, and sometimes all have them.
This is the correct usage taken beyond mathematics without the grandstanding. If the grandstanding form is synonymous with “notwithstanding”, maybe the correct form is synonymous with “after sorting into every”; but the next phrase must be a noun, not a circumstance or condition.
It is at this point we have to face up to the unsatisfactory use of the word “notwithstanding”, where some people follow that word with a precondition and others do the opposite, and give an exclusion. Others still just give the noun without stating inclusion or exclusion, but if you follow a literal logic, it should be an exclusion to the preceding statement.