Welcome to the Board, Maury! No worries here, everything on the board is Gluten free!
If I was going out west to hunt for agate for the first time I'd go somewhere named after me, too!  (Okay, I'll stop, promise.  )

Seriously tho, I have some beautiful old stock Maury Mtn agate but would love to see some of what's being found these days.
Are y'all lapidaries?
Back when more mining was being done Southern Illinois was the Fluorite capitol of the country. There are still lots of great specimens to be found in the tailing piles and around some of those old mines.
For more information and if you have never been the next place you want to venture to is Marion, Kentucky and the Ben E. Clement Mineral Museum. It's like a mini Smithsonian in the heart of the Midwest. They can also tell you at the museum what local mines are presently open to collect at. On a scale of 1-5, I give it a 10.
https://clementmineralmuseum.org/
Enjoy the ferry ride across the Ohio River there at Cave-In Rock!

If I lived up there I would also be looking in the Sparta area for old coal mine tailings to hunt for the incredible "Pyrite Suns". I wanted to stock up on those before the mining stopped and they became hard to come by but missed the boat on that one.

Love to see some pictures of what you've collected!

Oops learning curve. Picture of scale on quartz. Whiter material is the acid/iron out treated

Welcome to the RHL Maury. Well done for your first "get real dirty" rockhounding. As Joe said it will be real nice to see some of that blue quartz cut and polished. Since you already have the muriatic and since you have so many pieces to test I would try one piece just to see how it turns out. As Joe said Iron Out will be the best solution to clean most everything without too much worry of your specimens getting damage.  In this hobby there is a lot of experimentation but you learn the most that way.

I haven’t “noticed” any damage from the acid. Was just desperate trying to remove haze on crystal.  I bought a textile gun and it did a great job removing thick crust (?) off of crystals, crevices …. still a haze though.  Lost a lot of matrix with the gun, got carried away but many specimens pass light / glow now which isn’t bad.

Are these MM Agates what you have seen?   Not what I expected but pretty happy.

Very nice! I just wanted to add that many times when there is a coating of feldspar or other minerals it often leaves an etched surface.  This would be leaving the "haze" you're talking about -- which would mean that no matter how strong an acid you use you'll never get rid of the haze because it's not something that can melt off.  You would have to physically polish each individual crystal face, which of course would be either impossible or at the very least incredibly impractical. If you take a close look at the haze with a 10X loupe you should be able to see the microscopic divots on the quartz surface creating that haze.

Well, Maury, sounds like with all your excellent experimentation you are discovering the answers to your own questions! Good job!

That has been my experience at removing the “gunk”. Some of it will flick off with an x-acto knife and have a beautiful un-etched crystal surface beneath and some will take 3 or 4 or more soakings in acid or Iron Out, to remove satisfactorily, only to be left with an etched surface, and some will be partially included in the quartz and be permanent.
There are different types of “gunks” depending on the locality and mineral being collected, and it can be a decision whether to try and remove it or not. This coating from Maury Mtn looks like a secondary or tertiary coating of silica, or quartz, possibly mixed with feldspar, mica, and other mineral detritus that settled over time onto the crystals, which is why you may have gotten and initial reaction to the acid.  But Scott or someone may have a better explanation.

I'm still getting a kick out of you choosing your namesake mountain location to collect at,  ,  and I've done a little surfing to see what's being found out there today. I did see some pieces like what you found and yes, they are still finding the golden brown, yellow, green and red moss, too. Oregon sure makes some pretty agate!
Good luck and good job!