There are so many reasons to hit most of your shots cross-court in a match: early point of contact, the angle, the ball crosses low part of the net, it makes your opponent move more, etc. Another great reason is because a cross-court shot does not have to be hit nearly as well to be effective. You can also miss-time the shot slightly and still make it, as opposed to most down the line shots.
My suggestion is to just continue the cross-court shots until the entire down the line half of the court is open. By doing this you can hit your down the line shot to the middle of the open half of the court and not have to worry about being so precise with the timing. A down the line shot hit a little bit late is likely to be wide or long. A cross-court shot hit late is likely to be not quite as cross-court, down the middle, or even down the line, but usually in. A poor cross-court shot to an opponent on the cross-court side of the court is better than a poor down the line shot to the "open" part of the court, especially since the down the line shot is likely to land out.
Human nature tends to make us hit to the opening, but make sure it is wide open if you plan to hit your shot down the line.