When I made my lunches I used frozen bread and never had an issue with it going soggy. I reckon using frozen bread makes it less dry by lunchtime too.
I'd love to make Shel's lunch for her, but she leaves at 6am and I can never be @ssed to get out of bed that early I'm having an empty head moment but apart from ham and cheese (and it does seem a bit odd to freeze cheese...?) what other fillings could you use?