You have a lot of good stuff going on there and I am looking forward to a new version.
Given the number of systems you implemented, I can imagine that must have been a quiet stressful time for you. The crunch time in a jams is quiet taxing. That*s what I meant with when I said you where over scoping, I did not mean it to sound rude or make fun of you, just to highlight the overwhelming amount of work this must have been.
Actually you can easily store progress in Web builds using PlayerPrefs. That is what I am using to store the sound volumes and the highscore across sessions. Web builds will use the Browser IndexedDB to store up to 1 Megabyte of data. While it is strictly speaking not meant to be used to store game states, you can abuse it to store a single save game / player progression. Bear in mind that a versed player may be able to modify the content of the IndexDB but you can always encrypt/obfuscate the data before storing.
This is an incredible amount of work you put into this and it is a shame that this does not get the attention it deserves.
My hat off to you!