You can transplant. See the link. Transplanting during the growing season is discussed in the second half of the article.

Here is a link that might be useful: http://www.heirloomroses.com/care/transplanting-roses/

If you post this on the antique rose forum, there are many experts who can help you.
http://forums2.gardenweb.com/forums/rosesant/

Whether or not you decide to move it it would be a good idea to build a heavy duty trellis behind it that you can tie it to so it doesn't blow over again. My parents let their big china roses grow through a wooden fence so that the roses don't fall over in strong winds. Here's a picture of their mutabalis rose. You can see a little of the fence on each side of the bush. Of course growing it like this means there is just as much rose on the neighbors side of the fence as my parents side. It's good that the neighbors don't mind that.