I pushed the HTML5 zip file to GitHub! I recently discovered that the character is only movable in Google Chrome.
Overall, I can say that WebGL1 (that will be replaced by WebGL2 soon apparently) works compared to other shipping options: wasm and asm.js
Also, I switched from Unreal Editor 4.17 to 4.16 and uploaded the HTML5 from 4.16 version.
It's possible the version had nothing to do with anything and that I just needed to check the WebGL1 option, but just putting it out there just in case.
One last thing: I keep getting this message
"If you are the developer, make sure to deploy a minified Shipping build and consider migrating to WebAssembly for optimized memory usage.
Your browser or graphics card does not support the WebGL extension EXT_sRGB. This can impact UE4 graphics performance and quality.
Failed to read file UE4Game-HTML5-Shipping.asm.js from IndexedDB, error: IndexedDB not available!"
I have no idea how to deal with this, and there aren't many answers so far online, so I will continue focusing on at least decreasing file size for faster download. Feel free to leave comments post-jam.