I have a few spare plants of ‘Softee’. Mine forms lots of OP hips and its pollen worked on a few things too. Haven’t tried pollinating it yet… only grown OP seeds. If you send me your address I send you a few plants as they get a little more establish (they are newly struck cuttings at the moment).
Red Magic Carpet probably has Eyeopener as at least 1/4 of it. McGredy used it a lot in his 1990s hybrids, as well as used it further out as a grandparent in his 2000s hybrids. For example, his Candle in the Wind is 1/4 Eyeopener.
So, the answer is that Red Magic Carpet is probably part kordesii, mini, eye-painted and “other” 
The problem with McGredy is a lot of his hybrids that are not well-documented is that half of it is easy to figure out and the other half is mystery meat.
‘Softee’ tend to set tons of OP hips but rarely did I get it to sets hips as seed or pollen parent.
Kim selected this OP seedling. I’ve never tried using it. Once in a great while it will set a hip.
‘Softee’ pollen worked on ‘Wild Rover’ for me last season. Only a few seedlings up from this cross so far though.
Has anyone played with the thornless ‘Rosa setigera serena’ and can it pass on thornlessness? (Is that a word?)
pricklelessness? LOL
Of course.
And if it were on a young plant, it would be called precocious pricklessness, probably.
About Serena. In the article on germination (Home page, articles) I reviewed some old work of Stewart and Semeniuk in Beltsville, MD. They studied the germination of Serena, so it makes an abundance of seeds OP for sure. And it is very different from R setigera “Beltsville” CV. You might check whether Serena as offspring posted on HMF, and whether they pursued their efforts into breeding species types. They did introduce some specialty germplasm such as “spotless yellow” which seems to have been lost since then.