You're right that flannel or tweed would be not formal enough. But that doesn't mean you need to wear tropical weight either. A mid-weight worsted cloth would be your best bet. A plain weave, mini-herringbone or twill (even twill, not gabardine) would be best.
Bring one with you. Two of my friends who I visit regularly who request I remove my shoes now have a shoe horn by their shoe rack because I asked that they provide it for me. That's a must. I often have a shoe horn in my bad/briefcase just in case. I would assume that everyone here brings a shoehorn with them to the airport. I bring plastic so it's easier to go through the metal detector.
Chalk stripes are my favourite type of stripes, but unfortunately they are often seen as over the top in America. It can be hard to get away with anything other than a faint pinstripe in most business situations.
For an odd waistcoat with a charcoal suit I think that a buff waistcoat would look much better than heather grey since there would be more contrast. Heather grey also sounds dark for a charcoal suit. If it was a light grey it would work much better. Go with standard-width lapels. Narrow peak lapels will look silly.
Are there any television shows where people take off their shoes when entering the home, besides Mister Rogers' Neighborhood?
In Asian television and movies, do people always take off their shoes and put them back on when coming and going? It seems so important, yet it sounds like it would really make a movie lag, having to watch people tie their shoes.
White, light blue, cream and ecru are all great shirt colours to wear with a charcoal suit. Pink also works well too, if you're daring enough. And as far as other shirt colours with a suit, I'm not too fond of others, but some people like lilac.