Oh, I'm with you George is out! I also just see this classic making a resurgance now that the little prince will make a great name-sake.
Timothy "Otter" - Oh I think Otter as a nn for Timothy is darling and a great alternative to Timmy. Way to go! That said Timothy is probably my least favorite on your current list. I do like Timothy George or Timothy Lyle.
Charles "Chaz" - Love Charles, dislike Chaz. I actually really like Chuck but totally get how that would be weird with Huck. Is Charlie to obvious? I think adding a Charles/Charlie to your bunch would be rather charming. Charles Timothy or Charles Alexei.
Winston "Win" - My absolute favorite fn/nn option. (Though not my favorite name). I particularly like Winson Alexei.
August "Gus" - I adore August, it's just off my top 10 boys names and would actually be on there if I didn't have such an overwhelming A list. I find Auggie as a nn charming, fun and spunky. The only good association I have with Gus is Burton "Gus" Guster from Psych. This would be my top choice if it weren't for your nn pick. August Lyle or August Patrick are pretty darn smoking.
Patrick "Paddy" - I'd probably avoid the dashing Patrick as you already have a Philip and it would be the first time repeating a letter. Not that this would usually sway me from a great name but... your list has so many other fantastic options I'm grasping for any criteria to help me choose my favorite. Patrick Alexei (though this feels a bit like IRA meets Russian Mob) and Patrick Charles.
Edgar "Eddy" - What about Edgar? I saw him on your signature but not on your list. He is a little quirky but would work well with Francis. Edgar Florian would be pretty handsome, don't you think? Edgar Lyle?