Hi RN and welcome to the forum.
Some interesting challenges there and a lot to consider - more than I have time to work through right now but I anticipate others with similar requirements who already have solutions may be along soon.
My first reaction was to point you in the direction of Data Pump since you seem to have some volume of work here (assuming ths is not a once a year process ....) and Data Pump might just prove cost effective and give you all the controls you need.
My second thought was that if you use project exports you should (I think) be able to set up separate export jobs for each filter within the overall project export and then just run the project ( A very top level description which you have probably already investigated and found wanting but my reading of your description of the problem seemed to me to leave the question open ...). Or use multiple /px enties in the line to specify which jobs contained in the project you actually want to run. Or multiple lines, one per job, and then specify where they are to be sent, overriding the default if necessary.
My third thought moves on to your multiple model idea to observe that with Monarch V9 Pro you could develop one model as the master and then create and use other models Strongly Linked to that master model with substitutions for the bits that set different parameters. That way of the core model needs to change you change the master and the others will follow but retain their substitutions unless something breaks them. The linked models can be protect from changes other than via the master model.
I guess a fourth option would be to script something based on the input file name to change the name of the output once the export has finished - a stage in the process that would be external to Monarch.
As I mentioned back at the top I may have missed something here and it is a while since I have had to grapple with this sort of requirement - others are likely to be more recently experienced!