What you say makes some good sense. I hadn't considered it (right away) as an option, but it's on my list. My main concern is pulling too much out of St. Nazaire, especially as the Germans pile up armor. Then again, I have to keep in mind the stacking penalties as well.
2 infantry divisions with AT support should do the trick, armour has horrific penalties for crossing rivers.
And you have battleships do you not? If things get dicey, park them offshore and pound those Tigers to scrap metal with those. See how they like a 25% shore bombardment penalty on top of their 80-something% rivercrossing penalty or whatever it is for Harm. The only thing that I recommend keeping an eye on is the whole armour vs piercing. I don't remember exactly how AT stacks up against Harm. I know it works fine against Arm. But that is what the shore bombardment is for^^