So what do you do if you approach the other club early and they tell you they'll happily talk to you when the window opens but not before? Say bollocks to that and move onto your second choice?
Your strategy is sound up to a point, that point being where you haven't taken into account that there's another 3 parties who will all have their own strategy, and will likely only want to deal with you on their own terms.
Agents will want to tout their player out to interested parties, the selling club will too. Then the player will want to weigh up his options.
Whilst it is desirable to have these players in for the preseason tour, a handful of games, which are essentially PR warm ups, are not necessarily a guarantee that these players will magically gel. That's what the training pitch is for. So whilst I agree that spending the time with the rest of the team would likely help them to integrate into the team much better, it's by no means imperative.