[Buzz]

There are also some really nice Cobra replica manufacturers in the UK like Dax, for example, which was designed by the same man - John Tojeiro - who designed the original AC body that went on to spawn the Cobra; but I do get that you want a Cobra now to enjoy while you're in the US for a couple of years.
I may be mistaken, but I believe FFR (Factory Five Racing) manufactures RHD Cobras for sale in the UK and Australia. Maybe try them also to see if a UK-spec car can be bought, registered and driven in the US, then taken back with you when you return.
I also get that because of your limited time, you can't endure a long build time and would probably prefer to find one already constructed. Chances are slim, but they do exist. I'm not sure how quickly you could get a turnkey RHD Unique, FFR or Superformance on the road now, but others who have gone through the regular build process recently could chime in.
Good luck and keep us posted.

EDIT - If you're unsuccessful in finding a used example for sale, maybe consider buying an existing LHD Cobra by a manufacturer known to build RHD versions and have it converted. New dash using the same gauges, move the steering column over with a replacement RHD rack, some footbox modifications for more legroom and to accommodate the pedals and there you go. You could source the parts from the manufacturer and any number of automotive fab shops could handle the conversion. You'll probably need some changes for UK registration - marker lights, etc. - and you could have all of that done at the same time. Just a thought.
With my right hand drive Unique, I had no problems sourcing required parts from the manufacturer and elsewhere when I did a complete rebuild all the way down here in the Caribbean some 20 years after it was originally built. The only glitch I had was when I ordered new headers and sidepipes, I didn't realize how extensively the right footbox had been modified and the right side headers wouldn't fit. I had to fix that with some creative fiberglass/aluminum work and mods to the headers.