Thanks Steve. The photos on that link are like the four that I'm confident are John Hopper, as far as you can tell from full-face views. One of the features of John Hopper is that the outer petals fold downwards with time, so the bloom becomes almost a cube.
It's complicated by early mixing up of John Hopper with La Reine in Australia, but the two I'm interested in are not La Reine either. (Their study names are "Mylor Primary" / "Miller House Rose" / "Sue's rose", meaning that there are three sites in SA where this rose has been collected, and "Miss Curry" in Victoria.) The photos I took yesterday show quite foliaceaous sepals, but I don't think that's a definite discriminator, having looked at the others.
Follow-up: thanks for clarifying my thoughts on these! In the photo below, the cut and bud on the left are "Mylor Primary"; the cuts and bud on the right are John Hopper. I don't think the colour difference is significant, as John Hopper is at times the brightest rose in my garden. The more prominent downfolding of the outer petals in JH and its thinner receptacle may be. The stems are a convincing difference; young stems on John Hopper are smooth +/- with prickles, but those of "Mylor Primary" are bristly (shown better in the previous photo).