Our org got hit with an ADA lawsuit recently. Our group's focus is on the web side of the lawsuit, although it encompasses many other aspects. One problem is that there are no hard-and-fast rules for what an "ADA-compliant" website is.
Some honest questions here, as I am genuinely curious, as I'd guess you've already thought of these things and have reasons why they wouldn't work:
1. Is it possible to detect when ADA-compliance is required (e.g. detect when software is in use? Is it a different browser, or browser plugin that could be detected?) and present them with an accessible-specific site, kinda like how it's common to present users with a mobile-specific site? I have no idea about the technical aspects of it, but I think the compliance aspects of it would be analogous to providing both an escalator, and an elevator for accessible-specific use. You'd just have to make sure the accessible site stayed up to date with changes made to the standard site. Or maybe if not detectable, the first p tag on the page could be something like "Click here for accessible site"?
2. Is it possible to provide an accessibility specific phone number that they can call and have a human read the website out-loud to them? It seems like that might be cheaper/easier than redesigning a whole site in some cases. This would be analogous to gas stations with a sign that tells you to honk your horn and an attendant will come pump your gas for you, rather than having to design pumps that are accessible.