As for the deputy badge in question for Doc....
I preface with two statements:
1) Only today did I get an image clear enough to see the differences I list below. My apologies for not having found this earlier but I did try.
2) Right up to finding this photo and until one is cast,
JohnHolliday has made the closest duplication I have seen.
Here I draw my line in the sand. Screen accurate badges are not currently available, to my knowledge, including all that have been sold through the propstore as Originals from the movie. I won't budge on this unless photos can be provided matching the picture of Kurt I am posting here. All articles claim that all 10 deputy badges were the same mold. Either this is not an accurate fact or the badges being offered are not from the movie.
Given that numerous badges are proferred online as a match or even an original, the screencaps from the movie are my goto and my final answer, with a little waffling when someone offers poster pictures due to their inherent inaccuracy to the actual released film footage.
I finally got a higher resolution of Kurt's badge. It is the same as offered earlier but now with enough detail to solidly CONFIRM that:
1) there is no central star outline line printed in black within the cutout star shape but only the letters "U. S." with definite periods, NOT WITHOUT. The period for the S is falling off the edge but is present. If it is not falling off the edge it is NOT a match. The mold of the letters was obviously slightly shifted from the mold of the star or the smith's "U.S." Stamp was pre-assembled as that phrase. Meaning, they could miss slightly and hang the period but it is there.
2) There IS a circle printed near the exterior of the outer edge of the badge but is quite thin and disappears when the picture is blurry.
3) There are NO IMPRINTED STARS anywhere on this badge. None. Zero. Emphasis on "they are not there". Only one star pattern exists and it is the shape of the inside of the badge itself having the original circle cut through in five pie slices. I assume the aberation in the mid right side looked like a star in the blurrier pictures and matched the expected stars as seen on historic badges. They don't exist on this badge. (again kudos to johnholliday)
4) and now for the sad one, this is a SERIF FONT, meaning all the letters have the little wings and end cap bars at the extremes vs sans serif which are without the decorations. Times New Roman is an example of a serif font whereas Arial is sans serif but I will need to research further to get you an exact font if one exists. It could very well be custom and not a true font. 7 years as a professional typesetter and few fonts have eluded me since. Again, sorry I did not have a good enough photo to catch this earlier but it isn't even a light serif, it is heavy.
Further notes and my white flag of truce:
1) Assumption made: Kurt's badge is the same deputy badge as Val's
2) All previously found sources claim all deputy and circular badges on the movie were from the same mold.
3) Several posters were made with a mish mash of guns, holsters, coats, hats and badges that were not used by those actors in any scene but were instead worn by others or not worn, so the posters are not wonderful as a final answer.
4) This badge, though blurrier in previous pics, seems to be consistent for Val and Kurt.
As case in point, the image, as seen posted here, loses some important detail when viewed without zooming. Please open the picture and zoom in.
View attachment 1878184
View attachment 1878187
Here is the original vest 
