Billy, I did try to take some photos of the whole bush, but because it is sandwiched between a path and a HUGE General Schablikine, there just wasn't enough contrast to make any sense. I thought to get some old sheet to use as a backdrop to divide the Dr Grill and Gen Schab. which I'll still do. I'll post leaf, thorns etc shots for you in the meantime.

Yes, I would be thrilled to have a William R Smith with that provenance. Growing this would at least allow me to know if my Dr Grill is really W R Smith or not, although as I have remarked before, judging by photos alone they don't appear to be the same. Thank you. I'll PM you.

Billy, I've just added some photos. The first is the base of the bush. It seems to happily send up new shoots from just about anywhere on the old wood, which means I never have to be concerned about cutting it back, or thinning it out because you don't really have to 'keep the shape', so to speak - it will always send up new shoots. You can see that there is a single shoot coming up from the lowest branch and it has a hip on top. This is typical of the strong new shoots, although the new growth on the outside of the bush is more branching and twiggier than this with much shooter shoots. You can see what I mean about the awkward semi-hybrid tea-like growth, although I can't see this rose having any other hybrid tea-like qualities.
The second photo is a large leaf and the third its reverse. Most leaves are a bit smaller than this though.
The fourth, a bud I took yesterday. The fifth, the same bud today, and the sixth the same taken from the other side. The stems are quite smooth and glandless. They are always green for me. The last photo shows three hips. The hips don't colour much before they ripen, perhaps going a greenish yellow at most.

I did want to add that the colour of the foliage of my particular specimen of 'Dr Grill' is probably not its typical colour. I do have awful lime pockets in my soil and I struggle with chlorosis (as can be seen from a lot of my photographs).
At its best, the foliage colour is moderately dark.

My "Dr Grill" does bear some resemblance to the few photos of the 'Lady Castlereagh' from the Italian nursery Vivaio S'orrosa. I can't draw any conclusion but it might be worth considering this as a possibility, if theirs is correct of course.

https://www.saorrosa.it/il-cuore-della-collezione/le-nostre-t%C3%A8-3/lady-castlereagh/

I just found the photo of the bed of Dr Grill and tufted pansies in the Jekyll book "Roses for English gardens, and it is much more detailed and has better resolution than the copy in "The Garden". Unfortunately, when I upload a copy of it , it seems to lose a lot of the sharp resolution in the original which can be viewed very sharply here:

https://biodiversitylibrary.org/page/22558523

You can zoom in and see details of the buds and leaves, and blooms in various stages. I have to admit that there is nothing there that seems to contradict my version of 'Dr. Grill', in fact it confirms to me that I'm more likely to have the correct version than other Dr. Grills in the main Dr. Grill section here.
The bud receptacles seem to match mine, and aren't round like in the Moon painting. The buds themselves are moderately plump. The petals reflex like mine mostly do, and the flowers seem quite full, and the opening blooms look like mine too.
I'm about 90% convinced mine is the correct rose. Considering that this seems to be the only early photograph of 'Dr Grill' known, I think it should bear a lot of weight in correctly identifying this rose.