Well, I don’t do much cross-stitch (it drives me nuts), but I do a lot of needlepoint, which is almost identical in execution (except you don’t have to go over each stitch twice)
In needlepoint there are three techniques which form a diagonal stitch, and you have the same techniques available in x-stitch
All techniques go from the bottom to the diagonal top on top of the canvas.
Half-cross (what you probably use) Behind the canvas, go down one and start the next stitch to the right of the previous stitch. The thread forms a short vertical line on the back of the canvas. When you get to the end of a line, turn the canvas and repeat. You work the line from left to right. BTW, half-cross just doesn’t work on most needlepoint canvas, but isn’t a problem on cross-stitch fabric.
Continental: Behind the canvas, go down one and over two to the left so the next stitch starts one space to the left of the current stitch. The thread forms a diagonal line on the back of the canvas one space high and two spaces wide. When you get to the end of a line, turn canvas, etc.) You work the line from right to left(included for completeness, you probably wouldn’t use this for cross-stitch)
Basketweave: Behind the canvas, go down two spaces. and start the next stitch diagonally to the right and down. The thread forms a long vertical line. When you get to the end of the line, don’t turn the canvas. Instead, do the first stitch on the next diagonal line (at the same end that you are currently on) then go across two spaces behind the canvas to start the next stitch up and to the left of the previous stitch, forming a horizontal line on the back of the canvas.
In other words, you work the lines first in a diagonal going down and to the right, then in a diagonal going up and to the left. (With cross-stitch, I would turn the canvas a 1/4 turn and do the second round of stitches in the same manner)
When you finish, the back of the canvas has a pretty basketweave effect(with a tendency to be messy where two colors meet).
I don’t know about cross-stitch, but basketweave has these advantages for needlepoint: it’s faster and it doesn’t distort the canvas as much (and it looks cool on the back). It does tend to use more thread.
Does that make sense? I recommend trying it on a scrap before doing a project in it. Once you get the hang of it, it’s really easy to do.