goon I tell you what will help is if we're able to beat them with a mixed side
This is definitely something you could go round on, but this really isn't how this works in my opinion.
You play a "mixed" side against City away in this FA Cup tie, you likely get beaten. Then you've got no benchmark, and you can't benefit from instructing the fringe players who won't feature in the league encounters what they need to improve on for those.
You've also lost and in doing so you've established that your second string isn't good enough. The wider public interpretation of which is that you knew you were in trouble against City, so you threw the tie.
Play a strong side and lose, your players know the size of the task ahead in the league. Play a strong side and win, and you've got the psychological advantage, especially an away win.
You play the "mixed" or second string side when you don't care about the competition or you don't care about the opponent. In this case, we should care about both …