Thanks, buddy; your kind words remove anxiety about travel with old and new I797 confusion.I know this is your first time going through all this but it doesn't really matter. Until and unless you provide them your new i797 they do not know when is your last day and when is your first day at new job. So chill, travel normally like how you used to travel for your old work place.
Just last thing, do you have any experience with 1st time travel with Nexus card in Toronto Airport?