Why have a copy of a British gun when you could have a British gun?
$4K will buy a nice one in 12GA.
You should be able to pick up W&S Model 700 for well below $4k - here is a sub-7 lb gun with 30" barrels, good chokes and stock dimensions:
Model 700 I owned one and the only reason I don't still have it is that I am a dummy.
Sauer boxlocks are another excellent value if you find one in good condition. This one is overpriced, but you get the idea:
Sauer Since you asked, for my money, in that price range, I would buy a vintage Brit or German boxlock, Terry Wieland notwithstanding.
Hoof - PM sent, too.