To a large extent it is only a surface area exercise, in that I did not as you say look into fitting in the guns or the landing gear etc. However, I thought it an interesting exercise even so, since the drag contribution on an aircraft (especially one as clean as the Spitfire) is to a large extent driven by its wetted surface area which of course goes down proportionally if one decreases the wing size, thus allowing higher speeds to be attained.
In addition, a smaller wing leads to a positive weight spiral not only from the smaller wing itself, but also from lower loads leading to less material needed to carry the forces. So climb rate is also improved somewhat up to quite high altitudes, even beyond typical Battle of Britain raid heights (See figure on page 343 in book).
Now the wing profile is of course also important, and many attribute the low drag of the Spitfire as being due to its thin wing. However, the drag of the Bf 109’s NACA 2R1 wing profile is actually lower at high speed than the Spitfire’s NACA 22-series profile even though the latter is thicker, so there is more to it than that. So to make more space for guns and gear in a smaller wing, a slightly thicker wing profile like the NACA 2R1 could be used.
But for sure, trying to get the wing size down by means of a different slightly thicker profile and maybe even some small blisters here and there would require a lot of work. However, even so, if one premiers climb and speed, then a smaller sized Spitfire wing would have yielded higher performance I think.
Interestingly, AFAIK the Supermarine entry was actually in danger of being struck from the list for not complying too the landing speed requirement even with the original wing. However, the powers that be were duly impressed by the Spitfire’s performance, and it was allowed to stay in the race even so with known results.
As far as I can gather from his other design work, my impression is that Reginald Mitchell was not one to shy away from high wing loadings, and as I write in my book, if he had been given the same chance as Willy Messserschmitt got with the Bf 109, I would not be surprised if the Spitfire would not have been designed with a wing loading similar to the Bf 109's.
And if Mitchell would have been allowed to go for a higher wing loading on the Spitfire, then it would have been a much better performing aircraft than the Bf 109, which frankly relies a lot on its small wing for its performance. As it was, it’s impressive that it managed to match the Bf 109 even so, given that it was lugging around a wing that was all of 37% larger.