I'm still not sure why anyone would want to play with 3 centerbacks and a holding midfielder. That's as one dimensional and boring as I can imagine a line-up to be. I'd understand it if there was a libero type centerback in that back 3, who wants to move forward all the time and you need the holding midfielder to cover for him (dare I say David Luiz could actually be a very good player in that set-up). But if you play 3 centerbacks and none of them is capable of stepping forward and covering the space behind 2 box to box midfielders, the problem isn't hypothetically Khedira next to Herrera in midfield, it's a lack of the right players in the three centerback positions.
Personally I have no clue why van Gaal doesn't play a diamond. The players are way more familiar with the back four and Herrera and Khedira would be perfect players for the wide midfield roles in the diamond. And it would offer the same possibility of playing Mata as an AM behind Rooney and van Persie. The main difference would be that the weak spot in the team, the central midfield, would have an additional player and the gaping hole between midfield and defense would be filled. It would also give more protection to the defense than just adding another defender while letting the opponent run through midfield. Khedira all of a sudden would be a brilliant addition to the team with his energy and off the ball runs, when Carrick returns for the defensive midfield role.
But yeah, from what I've seen so far of United this season, Khedira isn't the right player to solve United's problems in that 352. I doubt Vidal would be either though, who is actually a similar player than Khedira, just better. But if it's true that van Gaal only plays the 352 out of necessity, not because he wants to, why would the club look for players to fit into that system anyway? Surely the players brought in should fit the tactics the manager wants to play, not the tactics the manager has to play right now because of an imbalanced squad?