Made them in the style of.... if you see what I mean.
Yes, Dee, I do see, thanks. However, those "arches" of tree are a standard for many artists- such devices were used by many artists from the Renaissance on, and although Reynolds used them, I don't think you can say that it's Reynold's style, unless you find something else as well. BTW, Reynolds was known for his versatility, and prided himself in his many "styles"- even Gainsborough gave him credit for being versatile.
I'm not saying it's not Reynold's style...just as I suggested it might be a pupil of Gainsborough who might have "painted" this, so it might also be a Reynolds knock-off.
I guess the only way to know which artist was being copied by the unknown technician who did these portraits for rhe BBC production is to ask the technician... no easy task!
] Mind you, we know that Austen knew the painter's work, but would she have been aware of his blindness and subsequent death?
As head of the Royal Acadamy and as the arbiter of taste for the masses, his death would have been known to almost everyone, I should think. He managed to cover up his blindness for a while, and continued to function as a lecturer, so perhaps that part would not have been so well known.