Correct, RL is more lenient on generic things, over there I have my X-Wing pilot and I have my Bith musician, for fun I combined the two and have a Bith pilot, all RL approved. That's how they do things over there, but that's not how 501st does things. Honestly there's a better chance of getting generic Nightsisters to be a thing (I personally would love to see that be a thing).
Over on the IOC a group of us tried to make the case that there should be a CRL for Thrawn's other ranks (Lieutenant, Captain) since they appeared in the comic adaptation of the Thrawn novel. After some back and forth, it never happened. Oh well, collectively we all moved on. These things happen.
You are correct that there is uniformity to the elements that make up the various Inquisitors uniforms. If this is really something people want to do, do it, make the costume and submit it to try and get a CRL made. Best case scenario it's accepted and made an official CRL. Worst case they say "sorry no", it doesn't become a CRL here but you could probably get it approved for The Dark Empire costuming group or just have a really cool costume for cons.
I'm not writing all this to discourage anyone from trying something, I'm just sharing my experiences with making CRLs happen (501st Bith musician was because of me) getting some shut down (see previous IOC story) and working on various detachment staffs (current XO for Gunners).
Every LMO team is different, what one staff allows/doesn't allow will differ greatly from what the previous and next team will decided. Nothing ventured nothing gained, if you don't ask the answer will always be no, etc