The "common" Douay-Rheims, a.k.a. Challoner revision (done in the 1800s) is slavish enough, accurate enough, and Trad enough for me.
If you look up a passage in the original Vulgate, and look at the corresponding Challoner English translation, you will find the same meaning -- the same content. It is slavishly accurate, without doing stupid archaic stuff with no payoff like using the thorn (The Y in "Ye barber shop" -- the Y is a thorn, pronounced "th", an archaic/obsolete letter of the English language/alphabet)
What is the point of putting the thorn back in? It adds NOTHING to the translation's accuracy. Likewise, it adds nothing to an archaic, other-worldly, sacred feel which you get with the Douay-Rheims Challoner. That one is PLENTY removed from the vulgar speech of today (grocery store, twitter, facebook, etc.). Honestly, if it were a notch more towards "archaic" it would start to lose serious practicality and usability (understandability, getting spiritual benefit from it, etc.)
Please don't try to be an Elite Trad among Trads. "Oh yeah, you think you're a Trad? You're practically Novus Ordo. You read the TAN Books Douay-Rheims? Well I read it in the original Shakespearean English. Oh yeah? Well I read it in the original Vulgate."
Ugh. Spend less time trying to be singular and stand out,
even when you don't need to, and spend more time meditating on the vices of pride and vainglory. No particular reason.

I know it's a foreign concept to NOT be singular in current year. Just dressing decently, not being insane makes you stand out to a huge degree. But when you're among sane TRADS, or at a Trad seminary, you should keep your head down, don't be singular, follow the crowd, and "do what the others do". See? It doesn't go down smooth, we're all shellshocked from living the last X years in the Modern World.
We breathe singularity like air and eat it for breakfast every morning. It's hard to know when to stop, isn't it?In other words, the arguments "But most people do it this way" and "But [the authority] says to do it this way" have been COMPLETELY annihilated for a few generations of Catholics. A casualty of Vatican II.