Ok.
I was doing some testing and you must definitely have some error somewhere else. I just created a stage with some meshes and textures and exported the project to HTML. The total of my files after exporting does not exceed 12 even though I have more than 12 files within the project.
Possible problems that occur to me are that you are exporting the project to a folder that already has other files.
Try this, when exporting, create a new folder, export ONLY the HTML version in that folder. (if you are exporting to another system like windows or linux, create SEPARATE folders for each export). When exporting, uncheck the option that says "export with debug". Check that folder and if you can take a screenshot. You shouldn't have many files. You compress that into a zip and try uploading it to Itch.