I hate to say this, but I certainly think Maggie is/was justified in her peck!
Yes, I hate the ones that walk backwards! Given their shape, they just 'slip right out' when they do that!! Next time, when you start wrapping, use a large towel and angle it a bit, pull the corner up between her legs from the backside, then wrap like a burrito. If it is wrapped snuggly (not tight, but not loose either) and you have pulled enough of the towel between the legs so there is the corner up by her breast bone, the rest of the wrapping will help hold it in place with friction, and it helps halt/delay the backing up. It took me a couple of tries with this technique to get it right...not too much towel between the legs...but enough to 'catch' under the rest of the wrapping okay. A determined backer-upper can still get out unless you wrap teh burrito part really snug (which I don't like to do), but it has, for me, given me enough time to administer stuff and or check a wound, etc before they can wriggle backwards enough to pull the corner free & back up.
Another hint...if you don't need to see the throat...
wrap burrito like, hold them like an infant child sitting on your lap. Bottom on you, feet/head facing away...one arm half wrapped around their body with that hand holding lower beak (head/lower beak) to open mouth. The other arm....forearm pressing against that side of chicken's body so they don't squirm sideways, while wrist & hand maneuver the syringe. It is actually easier than it sounds..if you are able to hold the bottom beak...to open the mouth...they will naturally lift their head, which is the position you want so airway gets blocked and 'stuff' goes down esophagus. However, they cant pull their head completely away from you as your chest/shoulders are keeping it from going too wild. (It helps if you 'slouch' your shoulders forward to create a bit of a 'concave' cavity that hugs them from the back and a bit from the sides.