Probably Dr Van Fleet. New Dawn is the reblooming sport.

I don't know how easy it might be for you to find Ilse(capital I looks like small L) Krohn Superior . In my garden this has been as close to perfect as a climber can be. It reblooms fairly well, is fragrant. I love the white blooms. I don't know how it will do in your zone, but I do know it is a Kordes rose. So it might be fine.
Climbing Iceberg is beautiful and gets big. It doesn't rebloom much unless the summer is mild.
Mary Lovett is a rambler with large white flowers.
You might consider the Hybrid Musk, Pax. You can train it as a climber.

Currently, I am enamored with Barfield White Climber and plan to get it this year. Thornless!

Here is a link that might be useful: Barfield White Climber

Try Sombreuil. Its an old fashioned beautiful climber and may be great for your zone.
I live in NY and the winter cold killed mine a few years back.

This post was edited by mikeber on Tue, Apr 9, 13 at 20:17