Lancs with Tallboys and Mustangs please in 1944, but we will discuss 1944 later. I completely agree with you all: Take out the Tirpitz first!
In 1943 things are going worse for the Kriegsmarine, it was the turning year, making it even more interesting in my eyes (it makes no sense to discuss the early years, only). So let´s start:
Early 1943 we have pretty air cover in Norway, Tirptz, Hipper, Lutzow, Gneisenau (and GZ in this scenario) as heavy units and some other smaller ones. (hi Trackend, you are right, only 34 RN- vessels but please take the non- british losses also into this calculation, there is one battleship sunk and 3 others put out of action by Fritz X) The US fleet brings in early 1943 the mighty Iowa into patrol position to protect the Atlantic against an outbreak of heavy german units. Barentsea remains the only probable theatre for the heavy german units. The King George V was put out of order for months (by accident). PQ-17 was protected by two battleships-Washington and Duke of Yorck (that is a battlefleet in my eyes). They were ordered back as soon as it was known that Tirpitz left it´s fjord. GZ would have made further damage to the convoi, it could succesfully lead other german units (like Lutzow) into convois. We know that Lutzow had problems to get in contact. Attacks against Tirpitz and GZ would consist of carrier based bombers (no torpedo bombers in fjords) and maybe some x-boats. None of them did manage to sink Tirpitz (while it is true that x-boats did put the ship out of order for months), why should it work on GZ? Possible: Yes. Probable: no. The presence of GZ would bind even more warships on the ETO, reducing pressure at the PTO. The sinking of Scharnhorst later in 1943 would be impossible, if GZ could succesful warn Scharnhorst of the presence of Duke of Yorck out there...Without the loss of Scharnhorst (debatable) Hitler would allow the reconstruction of Gneisenau: In 1943 were plans to refit Gneisenau (new and elonged bow for more lift and better speed, upgrade of its primary weapon (6 x 15 inch/52), radar and secondary weapons (22 x 5,1 inch multi purpose guns), it was even begun. The RN capabilities to take a heavy german ship out would be divided between Tirptz, Scharnhorst and GZ. I do not doubt that it would be more difficult to do the job. Another point has to be underlined: There is defensive for KM and the RN/US are pressing hard.Maybe someone can imagine a scenario between RN/US forces protecting a convoi and KM+Luftwaffe trying to take it out. Just for fun.