Withdrawing with the exit location as the destination can help get troops to the area and concentrated - having important elements fighting on the approaches can abort the exit attempt.
Once sufficient forces are near the exit, try to make sure that the exit location is secured - you cannot exit via a contested or enemy controlled objective, and try to remove any threats from being able to observe/fire into the perimeter.
Avoid having everyone fighting for the objective though - fresher troops will respond to the exit order quicker than those who are excessively fatigued.
Exiting small groups (Individual artillery Bn, or Bn formations of line troops is usually more successful than whole Divisions, as the larger units are far more likely to have someone in contact causing reassessments about how to extricate/protect/collect them.
Move HQ and support elements that are definitely moving after the lead elements are exiting (as a basic check that the objective is 'clear') so they can exit while the perimeter is secured, before his forces can intervene to block the route ~ these tend to be more easily 'stuck' be nearby enemy presence. Leave some forces acting as a rear guard to hold his forces away from the objective location while the bulk of the force disengages (withdraw or delay can aid in movement away from enemy in contact). Try resting during the afternoon and moving after dark if enemy fires have been a problem. Avoid exiting too many units simultaneously - traffic jams don't help, reducing movement rates over the areas affected quite strongly... so pace the movements so that a single 'group' is exiting at once, with other units moving to the area. These can be given waypointed exit orders, but I find that a simple 'withdraw' 'move' etc to the general area, followed by a 'simple' exit order often reduces confusion, and mitigates against miss-estimations in journey time or friction causing confusion where two units are both exiting together and getting in each other's way.
FAST is probably not needed very often - it mostly increases fatigue with minimal changes to journey times... having said that it can be useful for small groups to use to occupy vital junctions/crossings before the enemy arrives, while the bulk of the forces move via normal movement.