Seems quite easy to grow from cuttings. After 5 weeks there are four of the original six cuttings still alive. All are well-rooted and have been potted up (from a resealable bag). Two are pushing out plenty of new foliage. The other two each have several nodes looking like they will be producing soon.

Update: March 24, 2021 - One of the cuttings that was pushing out good foliage succumbed to rotting of the stem around the soil surface. Foliage was fine. Roots were fine. Stem gave up.

This seems to be a recurring problem with quite a few cultivars I've tried. Getting them to strike is often easy. Getting from there to an actual usable plant is trickier. They often succumb to rotting from either the bottom, or the top, or in one case even from a fork above soil level.

Thoughts on the resealable bag method of striking cuttings.
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Like anything it has advantages and disadvantages. Overall, I don't like it. Obviously this is personal preference, but as I see it the trade-offs go like this...

Pros:
1/ Yes, it will strike cuttings and, depending on various (sometimes opaque) factors, it may give a good strike rate.
2/ It requires minimal outlay for equipment.
3/ It requires minimal skill.

Cons:
1/ The bags are awkward to work inside (ie: removing a dead cutting, removing dropped leaves, dealing with fungus, etc).
2/ Due to the cramped space, it's easy to disturb cuttings without meaning to.
3/ The same applies when lifting a bag to check it, and putting it down again - this can cause the mix to shift and/or fissure.
4/ It's difficult to tamp the mix down evenly, due to the bags being, well, baggy, so cuttings may not be as secure as you thought.
5/ Humidity control is rudimentary at best.
6/ Even when inflated (a straw is the best method) the bags tend to collapse over a few hours.
7/ This, combined with excessive condensation, increases the likelihood of problems and makes checking the contents harder.
8/ And personally, I rapidly get sick of unzipping and re-zipping, and reinflating, large numbers of bags.
9/ This method depends heavily on single-use plastics. In principle the bags could be re-used, but...
10/ If multiple cuttings are placed in each bag, their roots tend to intertwine to some extent. This leads to some root damage when potting the struck cuttings, even if great care is taken. To minimise damage, tearing the bags open down their side seams is the best option.
11/ Strike rate achieved for a range of cultivars is highly variable, so this method is probably best suited for situation where propagation material is plentiful and wastage is not really an issue.
12/ For situations where material is limited and you really need to get a result, a more sophisticated method would be well worth considering.

One suggested alternative is to put the propagating mix directly into a storage box of some sort, and plant a large number of cuttings directly into that. This would still have to be covered to regulate humidity, but only having one cover per box is going to be much less hassle than a whole lot of individual, collapsing bags that have their contents obscured by condensation and have to be opened and resealed individually. However, the problem of root systems intertwining is likely to be worse, due to the larger number of root systems in the one container, with no barriers between them. And, unless the box is transparent, you have no way of knowing if roots have developed, or how developed they are.

This all seems to lead to an obvious conclusion: just stick the cuttings in square forestry tubes, with the tubes sitting in the standard 12 or 20 cell racks. The racks can drop into a suitable box, with a transparent cover of some sort arranged (ie: plastic sheet, standard propagation dome, etc). Or, make a mini-greenhouse large enough for several racks.

Forestry tubes will train the roots downwards instead of circling the pot, and air prune the roots at the base. They work for species that send down a thick primary taproot as soon as they germinate, and are capable of growing into trees 40 metres tall, so they can certainly deal with the average rose bush. When cuttings strike it is easy to check the base of the tube for root development without disturbing anything. It's not necessary to have transparent sides. You can feel when a tube is becoming full of roots anyway. By the time anything needs to come out of a large (70mm or 90mm) forestry tube it is going to be robust enough to be planted outside, and will easily come out of the tube without damage to the root system. Also, if a cutting dies or becomes infected it will be easy to remove one tube from a rack of them, and replace it with a new cutting if desired.

The tubes themselves can be reused for years, for striking anything that takes my fancy. To maximise success rate and minimise hassle, at a reasonable cost, this currently seems to me to be the best option.

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Update, March 11, 2021: One cutting of 'Lady Hillingdon' has been struck in a 90mm forestry tube, inside a clear plastic storage box (with lid). Went in on February 17 (ie: before the above thoughts were written). Showing promising root development just over three weeks later. The cutting that took had two mature leaves in perfect condition up top. The three other LH cuttings, that failed with the same method, didn't have good leaves. Am starting to think that summer cuttings without good leaves are hardly worth trying.

Seems to strike fairly easily. Received two cuttings 28/1/2021, and put them in a resealable bag. Four weeks later, one cutting had struck and the other had karked it. Small sample size, but the cuttings were taken and posted under heatwave conditions, which is a good test. You can probably bank on at least a 50% strike rate without any great skill being required (this was my first attempt at the bag method).

The struck cutting is currently being hardened up a bit in preparation for being potted out. I may try to beg another couple of cuttings, just to make sure I have a backup bush while they're both tiny.

This rose seems to strike surprisingly easily if you get a good example. I put three cuttings in a resealable bag on January 28, 2021. By February 26 all three were starting to show roots at the bottom of the bag. The cuttings were taken from an old plant, which presumably was budded before the cultivar was weakened by excessive propagation (if that legend about weakening is actually true in Australia).

The heritage roses article on propagation* says 'As a rough guide: for rambler roses, you can start looking for roots at 3- 4 weeks; for Tea roses from about 6 weeks. HTs, especially the yellows, are much slower and have a lower success rate.' Yet here is an HT, with a fair amount of yellow/foetida in it, striking with 100% success rate in 4 weeks. You can be lucky.

*https://www.heritageroses.org.au/articles/rose-propagation-ziplock-bag-technique/