While your suggestions are all going to be employed, and thanks for making them, of course we'll start with something I thought of. Because that's just how I roll.
Anyway, I thought it would be fun to take the player you voted man of the match from every game and study his performance through the chalkboards (sadly we can only do this in the league, but whatever). For Tuesday's match, you rightly selected Andy Carroll. After some perusing, here was the most interesting thing I found, his tackling:
To me, this shows a higher level of effort from Carroll than we've seen, and also what he's been maligned for. It's more of a shift put in than Luis Suarez in his last three matches before the ban. Now, I'm not trying to make the argument that Carroll is the dervish that Suarez is, or anything even close. But just trying to illustrate Carroll's upped effort level. No, he didn't win them all, but strikers rarely do.
The worrying thing, or something to keep an eye on, is his positioning. You'll notice how many of those tackles come around the center circle, and check out his heat map on his passing.
It's only one match, but Carroll isn't spending that much time near the box. It makes me wonder if he can really spearhead a 4-2-3-1 formation or a 4-3-3 if he's going to be floating between the halfway line and 18-yard box this much. Or is he going to need a partner at all times to get ahead of him? Can Liverpool provide wingers or withdrawn forwards who can get beyond him enough? Suarez and Bellamy would be the perfect candidates, but we've seen that not work before.