Saints expected to be very interested in former Cowboys HC Mike McCarthy [ Rapoport: Interview to be early next week]

This is an excellent point. I took it at face value that no coaches had won the Super Bowl with two different teams but did not bother to check how many had made it to the Superbowl with two different teams. You are right that it is 7, Shula, Parcels, Reeves, Vermeil, Holmgren, Fox, and Reid. I don't recall the details of the rest, but Vermeil was about a foot short of winning it on the last play. This makes it clear that the no coaches have won Super Bowls with two different teams is even less relevant than I thought when 7 coaches have made it with two different teams.
If you want to go back further Don Shula won a SB with Miami and a NFL championship with the Balt Colts. AND Weeb Eubank won 2 NFL championships AND a SB with the then AFL Jets