Attacking while moving over enemies with Carriers?

Solution 1:

When a carrier is idle or attack-moving, it will launch its interceptors against any hostile targets it sees in attack range (range 8). If it's attack-moving, it will also stop in place until out of combat.

If you issue a move order to a carrier that is currently attacking a target, it will continue to attack that target until it dies or moves out of interceptor range (range 14), but will not switch to new ones. (This behavior is inconsistent. If the carrier's target dies while the carrier is moving, occasionally two or three interceptors will not return and switch to other targets. I haven't been able to figure out the exact conditions triggering this.)

(Source of range numbers)

Solution 2:

When I am trying to run away with my carriers, I will often quickly alternate between attack-move and regular move. This gets them out of the way while still ensuring that they engage as they run. It IS slower than simply moving them, but it accomplishes the objective of getting them to attack as they move.