The Bonneville has a supposed 60 hp, will lug the heavy/square Ural chair about at 65 mph all day, maxes out with 85 on the GPS and turns in 45 mpg/140 miles range if you cruise with the trucks. The Sidecar is comfy enough for an adult passenger up to the fuel range and the boot/rack/pannier options would allow Elefant levels of gear to be lugged. All in all a fair BMW substitute!
My BMW R1100R, 80 hp, with the tiny plastic Meteor chair cruised at 70, topped out at 101, did 41 mpg/130 miles.
My Ural outfit, 36 hp on a good day, cruised at 45, topped out at 65, did 36 mpg and usually blew up before the tank was empty

Seriously, if you look at Urals make sure it's a 750 built after 2005, or its been owned by Tim for at least 10 years.
The big thing with outfits and range is the nut on the throttle. I can drop 10 mpg by going with the cars instead of the trucks

I'd say an XB type outfit would do the job, but is going to be slow. You have roughly 600 miles to do from your chosen port to the rally. If your outfit is cramped, lacks electrical power for heated kit and as a result you stop every 50 miles and average 30 mph, that's 20 plus hours in the saddle or over 2 days if the weather is bad. I doubt you'll sleep in the chair while it's moving, but two drivers will probably give you a few extra hours. Average 45 (that's what the Bonnevilles average was at the Dragon/Llanthoney according to the GPS) and you have two easy days and might well make it in one. If you are Mr. Morgan you can knock it off in 16 hours and still have the energy to ride up a ski-slope

. The thing is, the extra fuel a BM/Bonneville/Diversion type outfit will use is more than paid for in the hotel/food/beer if you use an extra day or two. Petrol despite evidence to the contrary is still quite cheap, a hotel room's worth is a lot of miles unless you are dead on your feet.
I'd totally agree with buying a complete outfit off e-bay. The Ural/Bonneville set up cost me something in the region of £2.5K to get to where it is now. If I had garage space I could have bought a decent enough outfit complete and still had the Bonneville as a solo. The price of a few new fittings and some wiring alone will make the purchase of a complete outfit probably cheaper, especially if you sort it and advertise as "6 months MOT, just did 1500 mile trip" when you get back.
Don't underestimate the amount of kit and what it'll weigh. You need two army sleeping bags, four sleep mats etc. In 2004 I filled a Ural body and a Touratech box with the wrong kit and was cold. I think now I could be warm with a Ural bodies worth of the right gear, but that does rather make a passenger a problem. I'd also worry about how warm you'd be in the chair, sitting still in a cramped space isn't good for the circulation and you'll have to share what electrical power you have. Sorry if I'm raining on your parade.
I'm plotting an attempt for 2009 or 2010. As this involves getting a new job, paying for the wedding, having enough left over for a decent honeymoon and then raising the trip money I'm not holding my breath

Andy