I would lean towards illegal formation for two reasons :
(1) It's easier to explain, "A lineman's shoulders has to be parallel to the line of scrimmage, and your snapper's were not." then ,"Because the ball has to be snapped by a lineman and, by definition, was not; it becomes a snap infraction and a dead ball foul."
(2) Illegal formation is a live ball foul and the play may not score even with the illegal act.
A couple of things to think of when the swinging gate appears :
(1) The snapper doesn't have to snap between his legs as long as the snap immediately leaves the hands of the snapper (7-2-4)
(2) Usually this is ran from the holder's vision side and the wing whose duty is that pipe should hold on LOS unless linemen then reset. We need goal line coverage for potential PAT and if the big ole' Bubbas decide to reset, the wing will have ample time to get to his post before they rumble to their new position.
IMHO, it doesn't hurt to ask the coach in pregame : "Do you run reverses on kickoffs or punts or do you run the 'swinging gate' on PATs ?" ---I don't like surprises