When designing an application, forget the visuals: design the flow of information, and the interactions. This is a surprisingly good facsimile for mobile-first thinking, as it follows similar principles: in both cases, you have a restricted amount of information to display, and have to design to deal with that.
Once you've got the information flow, step from there to visual elements, and ensure that as you build, you're baking in ARIA support and your testers are interacting with it using VoiceOver/JAWS.
At the end, the fact is you won't have anything perfect, but you'll have something better than the majority of sites out there. The reality is that perfection is impossible, but if you bake inclusive thinking into your app from the get-go, it's pretty straightforward, and you usually end up with an application that is less confusing and overloaded with information for your visual users too.
If you leave it as something to slap on at the end, it's almost always impossible.
The hard things like focus control require manual testing, ideally by a skilled user of AT.
I think you should really have someone who hasn't seen the app test with the blindfold.
Is that double blind, or just single blind plus literally blind?
I'm not sure how that would work for software, but it sounds like a much larger experiment than is currently customary.
Have you looked into pa11y and its CI integration [1]? It's a good start but it cannot replace properly testing your UI with accessibility in mind.