There are a lot of British doubles in America already. Buy the gun not the name. Each of the makers on your list made guns that should be right up your alley. You can find a worn out British double for less than two grand but do not waste your money. The search is half of the fun. If you can get to Las Vegas for the Winter show you can spend a couple days just looking and handling dozens of guns on your list. Find a good selection and pick the best shape gun you can afford. Do not fall in love with a Name gun with problems. They can be real money pits and a bargain gun gun could become the most expensive mistake that you will make this year.
I spent 20 years looking for one gun. Saw several with major or minor problems that I passed on. Finally found the perfect gun and bought it. Funny thing is that I never shot it worth a darn. But because my gun was in perfect condition I did manage to sell it for ten grand more than I paid for it after three years. Had I bought one of the earlier ones, with issues, I would have been luck to get my money out of it. The web is full of dealers with guns that they have had for years because they have minor of major problem. Do not take one of them off their hands.