Or at least has the Open Dyslexic font as an option.
I used to use Moon+ Reader with the Dropbox integration.
Have you tried BookFusion? I sync my Calibre library to it and use it on iOS and my android ereaders. Just checked and it has Open Dyslexic.
Does it work offline?
Yes, after you download a book to your device.
I’m using KOreader. It can use external fonts. I do not know whether it can sync or not, you have to check that yourself. It also isn’t ported to iOS, just linux and android. here are website and github page
This app, if it existed, would cause a war.
If it’s a full blown hot class war in the US, I’m in
I use an app called ReadEra which I like very much. I use the free version but it looks like the premium version does what you’re looking for: it can sync via Google drive and you can upload your own fonts. (Premium is a one-time $20 payment, not a subscription.)