] I...there's an airiness about the face which is very Gainsborough-esque.He/she might have been trying to do an impression of a Gainsborough acolyte painting Mr Firth-Darcy's portrait.

....a certain vacancy about the eyes of the Lawrence portraitees which isn't obvious in the Firth-Darcy portrait.

] Do we still want to assume it's an English artist that (a) JA would be referring to, and (b) that was being copied in the P&P production?

Since my imagination is fixed on the P&P Darcy likeness, as well as The Chapman Chronology and I'd like to think a British artist did the job, how about Sir Henry Raeburn? [Romney might have been another possibility. His style sounds "applicable", but he died in 1802.]
1803 Raeburn would have been 47 years old and able to do something like the splendid portrait of Isabella Mcleod which was painted in 1798(same year he had a a studio built - in Edinburgh?). I suppose he stayed with his customers - or would Darcy have visited in Scotland?
The simplicity of the portrayal with clean background, no details distracting the eye from the man, a human softness to face and a lithe impression of the entire figure. It's impressive, yet looks to be a human being not just a representation of wealth and tradition. JA:..."a striking resemblance of Mr Darcy, with such a smile over the face as she remembered to have sometimes seen when he looked at her."