Hi Drew,
I would still recommend using the Excel Import for this purpose. However do not let the end-users define the templates for upload, but let an admin define that.
Then the user can only upload their excels based on 1 or maybe 2 templates, but that means they first need to structure their excel according to that template. The most important thing is that the data is always in the same column.
If your challenge is in that all excel files are different then that is a process problem, that is hard to solve for to match all data based on the headers dynamically. That is why I would then suggest to move it around and make sure users are uploading the same kind of excel templates all the time, that Mendix can process.