Thanks for the replies everyone. I can get temporary residence in Denmark under family reunification, for two years. I can re-apply again after two years. The temporary residency is not the problem. The problem arises when I would try for permanent residency. Danish immigration law states that I have to be employed full-time in Denmark for 2.5 out of the three years proceeding the application. That is the sticking point.
I have just started the JAA conversion process - Bristol ground school. Every aviation job I can seem to find in the EU, as rare as they are, all require an EU passport, not just the right to work. And Denmark, being a relatively small country, has extremely limited opportunities in aviation.
I have taken time off from aviation in the past, and it took a long time to get back. In the U.S. currency is everything, I could be wrong but I imagine it is the same in the EU as well. Age isn't on my side either.
There may not be any way around it. I may just have to keep my job in the U.S. and commute (doable - I have a few friends who make the commute from the EU to the U.S.) and then worry about the residency/citizenship when I retire.
My other idea is to check into Sweden and their requirements. She is willing to move across the bridge to Malmo for a few years if that helps me get permanent residency or citizenship in an EU country.