Do it by the book for 150 odd pax boarding through one door and you will delay the flight by about 15 minutes. Most of the wrong aircraft scenarios are when pax have to walk from terminal to aircraft whilst boarding is taking place on adjacent stands.
I only said crew are meant to check it!
Do it by the book and you will have your back covered. If you delay the flight, explain that boarding time isn't obviously enough time as you need to check all that information on the boarding card.