There's something very wrong with the way the saves are coded. It's causing massive lag once you've saved about 25+ times.
I've tested both the apk file on Android and the html file on both Android and my PC just to see. The same thing happens with both clients in the listed environments.
It starts taking 30s just to open up the Saves window, and another 30s to save after tapping Save. 30s for the game to actually react after you tap a choice. The time grows proportionally with every succeeding save you make, so that by the time you're at 40+ saves, it's taking a minute for the game to react to anything you do.
Deleting all the saves does NOT fix it. It retains the massive accumulated lag. The only way to get rid of it is to uninstall it completely and reinstall the apk. As for the html version, presumably the fix is to keep clearing your cache.
This is a pretty awful bug as you can hardly just not save your game or keep reinstalling it every few screens.
P. S. Also, Save to Disk does not work on Android.