Actually, registering a replica is pretty easy in Oregon.
Rather than trying to explain it, go to this site and check around or send an email to the contact email on the site and they will help you out.
http://www.oregon.gov/ODOT/DMV/vehicle/titlereg.shtml
Where in Oregon are you located? We have a very active group of Cobra owners in Oregon- here in the Portland area and another group in Southern Oregon. In fact, we have a meeting this morning at 9:00 AM at landmark Ford in Tigard for the Cascade Cobra club and a run planned after. Good opportunity to see a lot of nice Cobras and meet some great people.
Bob