mike,
you did the right thing by replacing the transom, don't stop by not repairing the stringers.........they do alot for the integrity of the hull.....they do help support the transom. also help the hull from flexing to much. i guess the best way to explain is they are like rafters in a house. if the rafters are bad the roof falls in......everything in a boats hull are tied in together for a reason,strenght and integrity...
i don't think i would stop at the transom, you said you were concerned about the saftey of the boat, that is why you were replaceing the transom. this is just my opinion. if your not sure check with a couple boat repair shops........
good luck with your transom.......... ken

ps measure twice, cut once. :)