Hello Erasmus,
I have not yet tried this but maybe it will work for you. (At the expense of sounding like a broken record, since I just posted this for someone else.)

I came across this in a book I got from my local library. It's called "Secrets from the Jerry Baker Test Garden". On page 175 in a blurb called Share the Wealth, the author says to take a cutting 6-8 inches long, removing all the leaves but the top two. (It also says to do this after the plant is done blooming in the fall.)
After you do that, it says to:
"Stick the cut end into a potato, then plant the cutting (potato and all) with half of its length below the ground. Water thoroughly, then invert a small jar over it. Remove the jar the following spring, and you'll have a little rosebush, complete with roots. "

Thanks for the suggestion, Gardeninggene. I think that idea is similar to my idea in that the cutting is left alone for a longer period than usual. One difference in the potato method you mentioned is to try that in fall, whereas I root cuttings mostly in spring and summer. I guess I'll try making several changes, but I tend to think that since the cuttings do root, my problem has been that this variety doesn't tolerate being potted up as quickly as most. I might try the potato method on Hippolyte, as that one just doesn't put out roots easily at all for me.