Can anyone recommend a solution?
If you can enforce a common column-naming / data-typing format on all of the Excel files, you have a chance of using SSIS and looping to do this relatively easily. It still won't be easy - largely because Excel does not enforce data types.
But if you allow them flexibility, your solution needs to code around that flexibility - a lot of work - and SSIS is probably not the right tool.
If you haven't even tried to resolve your issue, please don't expect the hard-working volunteers here to waste their time providing links to answers which you could easily have found yourself.