I really like miniature roses, and have a few myself. My favorite is "Ralph Moore" - it is a deep clear red, with hybrid tea shape and moderate fragrance. But I think its flower is too large for your composition. Varieties come in and out of fashion that it is unlikely that you will be able to exactly replace the same cultivar. Since you are trying to restore a "work of art", it might be worth shopping the mail order catalogs and get a worthy replacement. It will be more expensive, but you have a better chance of getting the "right one". Miniatures can have flowers as small as less than 1 inch, to big blooms as large as 3 inches. The trend in hybridizing is often for bigger flowers.
Things to keep in mind, what size are the flowers of the original? If they are 1 inch or less, or are they closer to 2 inches? Flower size will be the most important thing to match. Flower color too. While you are selecting a replacement do yourself a favor and look closely at disease resistance, some are more susceptible to leaf spot and other fungal maladies than others. Also look at winter hardiness. There are hundreds available from various vendors. I personally refuse to buy a miniature rose that is not fragrant, for me, if it doesn't smell like a rose, it shouldn't be called a rose. But that is my taste.
I have bought from Heirloom Roses, they sell all their roses on their own roots, and do virus indexing, so they guarantee that the rose will be virus free. They are more expensive - $20 each, but you can pick out "just the right one".
http://www.heirloomroses.com/roses/miniature-roses.html?p=4