I have no problems with Craig's ... Cycle Trader is more trouble but once you know ins and outs of both, both doable.
With Craig's List search by City - Select: Motorcycles - Select: ALL (owner and dealer) - Select: Show Titles Only.
Use search term: DR650 ... do another search using DR 650
Go City by City. Searching "ALL" which will include dealers and private sales. If searching San Fran Bay are select ALL SF Bay Area. Same for Los Angeles area.
Getting your new title will be EASIER if you buy through a dealer.
They do it ALL for you. It's their job. Or ... don't change title, leave it as is ... just have it signed off by seller/dealer. Now you can register it in UK transferring from seller to you when registering in UK. (not sure about how imports work in UK)
You WILL need a local address to buy a bike if you want a new title with YOUR NAME on it ...you can use the DEALER's address in most cases. If private sale, ask seller to use HIS address. Should not be a problem. When paperwork arrives they can forward it to you via mail. (3 to 6 weeks)
If private sale you could do as mentioned above. Just take the bike ... and GO. (making sure seller has signed over title to you and done a bill of sale) Leave it in seller's name, sort it out once back in UK.
Don't get into buying for export, commercial or using MSO's or other machinations. A nightmare. Just do a straight buy like any punter off the street. Then just ship bike to UK. You might be able to "fiddle" the price you paid to lower import tax in UK. ???? not sure on this.
On a California title they ask you to list price paid. With a private sale you can put whatever price you like as long as YOU and the SELLER agree and the seller puts this SAME price on his "Release of liability form". They MUST MATCH or you'll run afoul of DMV. (this in California)
Dealers must put true price paid.
With dealer sale, paperwork will be filed with local DMV, processed, then sent out to you at whatever listed address. You will receive a new TITLE (aka Pink Slip), new, current registration and possibly a sticker for license plate.
As mentioned, if bike is going directly to UK, then none of this is required.
Private sale. If you decide to register the bike in YOUR NAME, you must appear at DMV (in some states) present old title, pay fees and tax and register your new bike. (Some states allow doing this all by mail).
Not sure about Oregon. The seller may be able to go to DMV and register bike in your name for you. Not sure on this, should be doable in most states.
I know it seems complicated ... but really it's NOT!
Good luck!