Your description is a fair reflection of the photograph but quite differerent with regard to colour from Ellwanger's description in "The Rose": "Vermillion-red, shaded with crimson..."
Looking at the references for this rose, I'm wondering if there is adequate evidence to add Comtesse de Choiseul as a synonym? I would be tempted to do so but would like corroboration that it is appropriate.
Ellwanger is the only author who sees 'Mlle Marie Rady' as vermilion-red, the early descriptions are "bright red, white glazing on the circumference".
Regarding the synonymity with 'Comtesse de Choiseul', we need to be very careful. It was "declared" synonymous around 1896 due to its similarity. At the time many roses were already mixed up in nurseries, so the French Rose Association declared many roses as synonyms. In our today's view, these are not synonyms, because they were bred at different times by different breeders and have often known different parentages. We indicate this so-called "synonymity" with a note indicating the similarity.
Thanks, Jedmar. I obviously did something wrong before because when I did a search for Comtesse de Choiseul I came up with nothing, which made me think (wrongly) that that name wasn't even in our database. Since I now see that that was my error, my inclination to make the two roses synonymous no longer seems like such a good idea.