Try bundling your assets into a .rpa archive. People usually do it for copy protection, but it could solve your problem as well. Though come to think of it, the resulting file might be too large, and bump against another limit.
Please consider only making a demo playable online, and offering the full game for download. That's the best approach.
Thanks for the fast reply! I already archived all my image, audio and rpy files, but the number of files barely changes.
Even my test project with no assets at all suddenly has more than 1.800 files...
After extracting the .zip folder of my test project "Testing" (2 lines of dialogue, no images, no audio), I get these folders: game (93 files), lib (566 files), renpy (465 files) and Testing.app (538 files). This project hits the file limit even though it has no content.
You're definitely building your distribution incorrectly.
From the Ren'Py launcher (latest version), select your project but don't click Build Distributions. Instead, click Web (Beta), then Build Web Application. This creates a directory with a bunch of stuff including a game.zip file. Ignore everything else and upload the game.zip file. Correction: you need to upload the entire directory, packaged as a zip file.
The Build Distributions button is for building downloadable games, not web games.