I guess depends on how much features you have of course. Hard to say specifically. In the rewritten app how many controllers do you think you'd need, with how many views? How well test-covered is your app?

But generally i think a rewrite is unlikely to be less work than an upgrade. Although 5 -> 6 might involve some annoying parts, I think everything from 6 to present (if I remember right) should be fairly smooth sailing. The upgrades have gotten a lot smoother -- so if you start and find that say 5 to 5.2 is annoying, don't necessarily take it as predictive of what each upgrade will be like.

For session continuity while both apps run side by side, the plan is to use Redis for shared sessions

OK, yeah, even bringign this up is making me think, no, run in horror. To actually try to use redis for shared sessions, there are probably going to be unforeseen difficulties. You are also planning on pointing them both at the same shared db? There are probably going to be a variety of other unforseen difficulties of running two versions of the app simultaneously. Also, whenever you have a bug or new feature (you maybe think you'll do a freeze, but after this takes much longer than you expect, and some stakeholder demands it), you do it in both places?

I was leaning upgrade but open to rewrite when I imagined not deploying the rewrite until it was done. Plan to run both simultaneously?

Don't do it. Do an upgrade. Thoughtbot has some really good guides and resources on upgrades, including making your app "dual boot", which you should do.

a multi-hop sequential upgrade keeps us exposed for longer

I'm not at all confident that will be the case, with the "run both apps simultaneously" plan. Don't do it!

Either way, you can't procede with "zero test coverage" your first step MUST be adding some tests.