Kyla..........
It sounds like you are doing a lot of things right to reclaim this garden. Good for you !
>>>>it put out a great number of red old-fashioned looking blooms, in May and June.
Without photos of the blooms, it is a little hard to determine whether or not the rose has reverted to the root stock called Dr. Huey. Dr. H was a really good rose in its time and if properly cared for and if you don't mind a once bloomer, it is still a good rose. It has certainly proved itself to be a survivor under less than ideal conditions ! The reason most people are unhappy with it is because it is a once bloomer and the rose that was probably budded to it has died, thus it is a symbol of failure of a rose to grow.
Dr. H is a climber. At its best it is more effective if used as a climbing rose rather than a shrub rose. In fact, you might even enjoy the rose more if you trained it to go up the trees you have laced. Then you don't have to mess with the established root system and with water and feeding and training, the rose can put on a spectacular show during its once bloom season. Dr. H will reach for the light and be easy to train up a tree.
You may want to save your full sun spot for a repeat blooming rose that may give you more pleasure throughout the season, but that depends on you
If you decide you still want to move the rose to a sunnier site, I would suggest that you wait until spring to move the rose. Yes, you can do it it in August, but you are setting the rose up for more stress and you have already said you have lots of other things that need your attention.
There are a couple of reasons I prefer to move roses in spring rather than in fall. In either season you are going to mess with the root system and that does create stress for the plant. Dr. H is very good at growing roots which is why it has been the chosen root stock since the 1930s, if your rose is Dr. H., so that won't slow the rose down too much. More importantly, photosynthesis slows down in roses when temps reach about 70F. Which means that the foliage will not be producing sugars to feed the rose naturally. Also, I don't know your winter temps, but encouraging new, tender growth going into the winter months, just sets that new growth up for die back.
If you want to get a head start, you can dig the rose hole now, put a container in the rose hole and put your back fill into the container so you don't trip and fall into the hole and the planting hole is ready for spring. You can then cover the whole bed with more mulch which can decompose and feed the soil over winter.
Another advantage of prepping the hole now and waiting until spring to move the rose is that you can see what the roots of that fig is going to do. Figs generally are considered fierce competitors and develop a dense root mass that is very, very good at stealing moisture and nutrients from nearby plants. Note: Be sure to perk test your planting hole. Ideally, according to most rose literature it should drain within a couple of hours. In my experience, if it drains over night, the rose will be fine.
>>>I know the root system will be very wide -- is it also likely to be very deep? (watch me cringe.)
No need to cringe ...
You do not have to transplant the whole root system, even if the rose is not Dr. H. To transplant the rose, you will cut back the top growth to make it more manageable. the root system does not have to be any larger than the remaining top growth.
Roses grow their roots first. So, it will look like your rose is just setting there doing nothing, but there is a LOT going on under the surface of the soil. Just keep it watered and fed and it will take off when it is ready.
>>>My main questions are about the size of the root area, and whether this is really a stupid idea altogether.
No, it's not a stupid idea. I am thinking that the rose has proven that it can survive in less than ideal conditions with little care, why not give it a chance to show you what it can do in that spot with some attention and training ? A healthy Dr. H can knock your socks off !
Smiles,
Lyn
