[ , I have trouble playing white keys in between black keys, if my fingers were a bit narrower, this would never be an issue.[/quote]
Yes Pete, I think you need an adequate hand size to play the piano or to be a best provided your brian and nervous system work well with it.
I can only just reach 10th, but my fingers are narrower than yours, so no problem to play in between white /black keys..
With my own expereince and my friends in concert profesion so as other well known pianist, it seems a broader hands is the factor rather than long fingers. Claudio Abru is one example. Idret brett(slim but agile hands)
Ramaninoff is one of the unusal hand span 12th. but so as Willham Kemp. Shoberg...
How about Yuni Li and Lang Lang, I am sure Yunis hands is not large but managed to win 2000 Chopin international piano competition in Warsaw.
And 2nd in Liszt competion.
So my conclusion is, you can only DO WHAT you have you got. Its the gift from God.