I looked at the link to the updated one, and liked it better "before" than "after." So it could be my opinion is exactly what you don't want. That said...

Necessary changes:
--Change the cog on the hub. It came with an 18T, you want a 22T. Well, maybe a 21T or a 23T. You may have to add a link or two to the chain.
--Change the brake pads --just the rubber-- to CoolStop salmon ones.
--Get a longer seat post if necessary.

Optional changes:
--alloy rims, either Sun CR-18 (better) or Weinmann (cheaper); but only if the existing ones can't be trued.
--saddle. Most people would suggest a Brooks B67, I think, and I'd agree.
--flip the handlebar and see how you like it that way. My guess is you won't, but it's fun to try it for a while.
--alloy stem and alloy handlebar if you already have them lying around; you might save an ounce here and there (hardly worth it).

Don't change:
--fenders and chain guard; they are functional and give the bike its classic look. Without them, it's ugly.
--wheel size. There's no point.
--crank; I know, it's a boring one, but changing it is a lot of work and expense for very little benefit (a couple ounces, I'd guess).