Well I finally finished the endless dungeon, though yee gods it took some grinding, and even with 6800 strength and 3600 health it was tough. actually by the time I got to the nineties and was facing over 3k Jerks at a time I finished up just farting my way through :D.
Sadly other than the hall of fame there didn't seem to be a reward, which was mildly disappointing since it did take a lot of resource gathering to get all those upgrades, although as the game gets expanded there will likely be more to do of course.
Two things I do wish, is that there was some sort of indication of the relative strengths of the Jerk's you face, since I lost out in dungeons fairly often when, even though I had more health than there were jerks, the jerks were obviously doing more damage. Even if you didn't want to include the jerk's strength, a single one word indicator of relative strength as to whether the jerkes were either stronger or weaker than Derekk, so how much health might be needed could've been helpful.
I also would've liked a way to trade stardust in higher amounts with the stupid planet, since having to constantly hammer buttons to pay ten stardust a go when I've got over 7000 got very time consuming. Actually, it'd be nice to have some stardust options for Derek, since the other resources are all used to buy his upgrades, or maybe something minigame wise to play (I loved the little games with the brockley empire like the stock exchange).
As to browsers and screne readers, you've actually already implemented many of the things are good for screen reader use, EG headings and buttons for web controls, without any annoying bits such as mouseovers.
I am guessing one problem on Ios would be that notifications in the game which disappear and reappear, such as the slots results wouldn't be automatically read by voiceover.
In the browser these aren't a problem since none of the text disappears too quickly, and it's easy enough to just press up arrow to read the line above a button to get the slots results.
This is one reason why I tend to prefer navigating web pages on pc, since its far easier when you've got handy shortcut keys to jump to next button, next heading, next edit area etc, than on Ios where you'd need to swipe, or to change the rotor control.
You might consider looking at having notification texts automatically output to voiceover, or putting them in popup on screen boxes.
Hth.
I'll be looking forward to chapter 3 and new editions to the game, it's been a really fun ride, even if those endless dungeons were a bit of a slog :D.