I'm not even done with my game yet and I'm having issues where the loading speed online for playing my game is really harsh. I don't really want to have to ask people to download quest in order to play my game smoothly.

Are there any other websites that host quest games or a way to host the quest game yourself? I've looked a little bit into hosting it on my own but I haven't gotten a straight answer.

You can check following pages:
https://textadventures.co.uk/forum/samples/topic/3irw80wjz063-no46fiymq/how-to-make-a-quest-5-game-run-on-a-private-server-step-by-step-with-screenshot
https://leewardslope.com/hosting-quest-game/

It seems to work but the player can't save while playing

Thank you! I'll look into these!