One of the lessons I learned from legends like Dan Seemiller and Dave Sakai was the value of down-the-line training. When you hit crosscourt, you have about ten feet and 3.5 inches. Down the line, it's only nine feet, so 15.5 inches shorter. If you can maintain an aggressive down-the-line attack in a drill, then going crosscourt is easy!
Often the simplest drill is the best. Just have one player hit or loop forehands down the line to the other player's backhand. (If you have a righty and a lefty, then it's forehand to forehand and backhand to backhand.) Drive the ball aggressively deep and as close to the side-line as you can. Often the forehand player is the aggressor, the backhand player blocking, but the backhand player should also learn to be aggressive with these down-the-line shots.
When hitting or looping backhands down the line, face the direction you are going. You can make last-second adjustments in a game sometimes to throw an opponent off, but by the time you start the forward swing, you need to be lined up for the shot, especially the shoulders. The exception to this is when just blocking against an opponent's aggressive shots, where you can just angle the racket side to side to change directions.
When hitting or looping forehands, you also want to line the shot up. This usually means more shoulder rotation and taking the ball a little later than usual.
There are countless drills where you can incorporate down-the-line shots, but start with the simplest, simple down the line. Then you can progress to other drills. Perhaps have one player hit side to side while the other alternates forehands and backhands, with one of them crosscourt, the other down-the-line.
After doing lots of down-the-line training, two things will happen. You will be able to do it in a match, and you will find crosscourt surprisingly easy, with that extra 15.5 inches!