There are shortcuts available on IOS through the shortcuts app. I know there's a gif maker, maybe you could find one for making memes, too? Might be worth doing a google search for a meme maker shortcut. I don't understand why you couldn't share the photo, though. Whenever I've played around with pics and markup, there was always a share button which would allow me to text the photo, save it to camera roll or files.

Wait, markup is accessible? What?
Fellow blind meme lover here, I love scrolling through r/Dankmemes or r/HarryPotterMemes and some others with seeingai but never thought actually using markup would work lol. I should try that.
Can't answer your question about saving, though. Is there not a share button that allows you to save image? If not screenshotting might be your only option, as annoying as that is.

I have no clue but this sounds so cool! Upvote and I'd also like to know this.