I know that Botham's record was surprisingly modest. However he could open the bowling and take wickets, and I'd like to see him batting explosively in the same middle order as Freddie. Plus I'd want him in the team because he's simply a top-class all-rounder and you can't afford to leave him out. When you look at the replacements (White, Daffy) you start to realise how true that is.
As for Gower, well I'm an enormous fan of his, and he certainly played some good ODI cricket: he had an outstanding series in 1982/83 in Australia, and was a great fielder in his youth. But I'm afraid to say I pigeon-hole him as a Test player. Hick has a better record and would offer an option with his off-spin as well. As a fielder, he had an awesome throwing arm and was IIRC a competent out-fielder. His main fielding position was at slip, of course, where he was one of the very best I've ever seen, but ironically he might well not ever get to field there in this team given the presence of Botham and Freddie. So Gower, as a specialist cover fielder, would offer more in the field to this team. All the same, I'd have Hick due to his track record with the bat in this form of the game. I think. Actually, the more I think about it the less certain I am... Erm...