Alright! Sample 3 arrived today, and I have to say...I'm pretty damn happy with it overall. I took photos of it under several different types of light, and I'll go into more detail on my thoughts
after the pics, so as not to influence your opinions.
White LED bulb
Direct sun (I took two pics here to illustrate how the color changes based on the viewing angle, which is intensified in the brighter light)

Indirect sun
Even-less-direct sun + incandescent light (specifically attempted to adjust the white balance based on my skin tone)

Warm incandescent light (after the sun went down)
My thoughts:
- The embroidery looks amazing to my eyes. I can identify a couple of spots that we had mentioned in our feedback, but seeing it in person at its actual size--rather than blown up to the full height of my monitor--they're definitely negligible.
- I'm a lot happier with the yellow thread than I thought I'd be. A bit less orange than we were leaning originally, but I think this is quite accurate to what the prop would probably realistically look like in proper white light. We
could ask them to switch back to the Sample 2 yellow, but now that I've seen this one in person, I'd be perfectly satisfied with it.
- When viewed head-on, the blue is nearly perfect. However, it's got a borderline-metallic sheen that causes it to shift colors pretty dramatically as it moves. I
suspect that's not accurate to the prop...but I don't think I'd call it a dealbreaker.
- Somewhat depending on the lighting, the tree trunk comes across more like a burgundy than a brown. The perfectionist in me is slightly bothered by that, but it's so close to brown (and such a tiny portion of the patch) that I don't think it really impacts the overall look.
I don't know if the existing minor issues are worth the hassle of going back to the drawing board and having more samples made. How do y'all feel?