Your question raises a number of questions, but here's what I have so far:
If you are buying the bike in the UK you are better off to get the carnet in the UK, from either the AA (Automobile Association) or RAC here.
The AA in UK will issue a carnet for non-UK residents and non-UK vehicles, which is probably the most 'casual' of the auto associations that we're aware of!
You can reach them at +44-1256-493753 or by e-mail: email@example.com
. They can fax the application forms to you, but will require originals to be mailed back to them before issuing the carnet, so allow time for that.
I don't know whether you can actually register the bike in the UK before you are physically in the country, but it sounds like you've checked that already.
If all you need is a mailing address, Mailboxes Etc (a US chain) will rent you a mailbox which you can use for this purpose, and they will forward it to wherever you like or hold it for pickup. There is one in Windsor (near Heathrow), which we are using. Contact Robert MacMillan at firstname.lastname@example.org
or +44-1753-775797 and he can make all the arrangements by phone and fax.
You should be aware that when your trip is finished, the bike will need to be returned to wherever the carnet is issued from, (which is usually where it is registered). Or if it is permanently imported into another country, you must have the official customs receipts from that country, showing all duties and taxes have been paid. This is so that the carnet can be discharged and you can get your deposit / guarantee back.
Hope this helps. Good luck!
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