The RN was not quite as overstretched in WW2 as you make out, not least because the RN had substantial naval allies, bases all over the world and a large fleet of smaller ships. For a time in 1940 it was in a difficult position, given the threat of invasion, Italian entry into the war and lack of radar. From the autumn of 1940 Britain was dominant in the Med in terms of surface ships and techniques in operating against raiders were being developed which came to fruition in 1941 onwards.
I disagree. The home fleet had more assets in 1940 than in late 1941, attrition in the different theatres account for the differences in naval assets aviable. But the most important consideration may not be a BB, which is to slow to track GZ anyway but a carrier. In late 1941 sceanrio only VICTORIOUS is aviable to the home fleet, the situation in 1940 was more relaxed. I also guess You overstate the effectiveness of anti-aider tactics developed by the RN in 1941. Only once they were effective against BISMARCK and a number of people make a case that this was as much a matter of luck as it was a matter of planning. BISMARCK very nearly escaped and PE wasn´t tracked, either. If You replace GZ with either of the two ships then the RN can´t make successful intercept and are in deep trouble.
You also ignore the cases when the RN went out to search for raiders but failed in forcing them to action in the North Atlanitc. That happened in 1939, 1940 and 1941 more often than not.
Using GZ against single unescorted merchant ships is a waste of resources, a job for hilfskreuzer. Its purpose should be convoy attack, and in doing that it reveals its presence and puts it under threat of counter-attack from a variety of forces. Like Glorious, it could in por visibility simply blunder into enemy forces. There are plenty of opportunities for things to go wrong, particulary if its aircraft are already attacking another target. How does GZ deal with a Chilean Reefer or a Stephen Hopkins? What if it finds an RN Q ship? What security does it have against night time attack?
Attacking unescorted merchants is a legitimate target of war, much more valuable than sinking a cruiser. Airplanes can strike merchants, they may also strike merchants in a convoi. HX convois often had a tanker or troop carrier with them and Ju-87 and Fi-167 can make short work with such targets. Unlike a battleship or cruiser as a raider, which is dependent on gun action, these airplanes can afford to ignore the escorting R-class battleship and directly go for the important targets in the convoi.
-now I´m waiting for the one who is telling me that the old R-battlewaggon projects effective AA screens over the transports while GZ is unable to provide effective AAA for herselfe, despite beeing better equipped for this task-
Fw-200 operating from Brest, long range maritime fyling boats and submarines scout vast areas of the mid Atlantic narrows and the western approaches and report sighting of convois and enemy movements.
I am also confused where You take Your "variety of forces" from? Home fleet in the mid Atlantic? They need to refuel by that time- the sorties of 1940 and 1941 (including operation Rheinübung) painfully underlined this point, cruisers and battleships in the RN didn´t had the legs to stay in the operational waters for any time following a chase. KGV, VICTORIOUS and PoW emotied their bunkers trying to follow the movements of BISMARCK, they couldn´t even think of continuing the action and look for PRINZ EUGEN, which was on the loose somewhere in the mid atlantic. How can You ignore this?
In the whole argumentation it seems to concentrate around what may go wrong for GZ in such a sortie. I do not question the high risk profile of a lone raider. That was true for all raiders sent by the KM. As mentioned previously, the KM had to reckon with the eventual loss of any raider sent out alone.
But really, what I am missing is a convincing theory why the RN would be able to track or pin her down with aviable naval assets in late 1941. All I read are broad statements like:
GZ would have been countered effectively, just as Japan's carriers after the attack on PH all came eventually to sticky ends.
-which in my eyes only expresses hopes and whishes but no factual base why this could be expected inspite of the difficulties faced by the naval force executing Sea controll.
Instead I challange the task force view. The german fleet had no buisness with task forces in ww2 and GZ had nothing to do there. If the true goal of the operations in the North Atlantic were solely commerce raiding with a goal of interrupting Britain's supply lines, then I would say that forming task forces around a carrier did NOT make sense. Sending out a Graf Zeppelin centered Task Force to roam the open ocean in search of individually-sailing merchant ships would have been futile indeed. What were the rest of the squadron supposed to do while one of their squadrons searched and sank the occasional tramp steamer they jointly came across? Britains forces are stretched but against a concentration of forces it may concentrate on her own, knowing that little else needs to be cared about in the Atlantic. Britain had a substantial superiority in capitalships and as I suppose, had an experience advantage, also. In 1941/42, ww2 had long since seen the introduction of convois and the only reasonable purpose to sortie that many capital ships as a group would be to overwhelm a heavily defended convoy guarded by heavy ships in a major naval battle. A task force centered around Graf Zeppelin should include the twins preferably then. But still, this doesn´t make much sense to me. A Task Force is an attractive target and the RN repeatedly showed it´s ability to trap forces. And GRAF ZEPPELIN is simply to fast to be slowed by a BISMARCK, a HIPPER or a SCHARNHORST. If it ties on these ships, it may very well tie itselfe to their fates. Logistical problems accumulate. While it is not much of a problem to keep a single or two heavy units fueled and serviced with a very redundant logistic fleet train, a complete Task Force stretches the KM fleet train to it´s limits.
A unified squadron made up of BC´s, CA´s and Graf Zeppelin would have been forced to spend the majority of their time between regularly scheduled meetings with supply ships to keep their bunkers full rather than aggressively running down every ship on the ocean to send to the bottom. There is less redundancy in tankers and more tankers which on their own may be subject to attacks. While a single carrier can be served without big problems a whole task force is an entirely different matter and reduced redundancy directly relate to higher dependentness and thus less tactical flexibility.
When it comes to destroying merchant ships there was nothing that a carrier could do out on the wide Atlantic that a couple of light cruisers on the loose couldn't have done equally well, except that Graf Zeppelin projects a larger effective fighting zone into the Atlantic with air ops. This advantage is crucial and devaluates the other big ships. What are You expecting the german admiral of a GZ + twins task force is supposing to decide when his scouts tell him a convoi made up of 20 merchants and an old battleship is sighted 80nm to the East? Do You really think he orders the twins to engage? Or isn´t it more likely that he orders the carrier airwing to strike? But then the role of the twins has already been degraded to mere escorts instead of raiders...
Other situation if the reason was to send out GZ onto the broad Atlantic sea lanes in order to disperse the Home Fleet, then it doesn´t need to be covered by big ships but instead could operate independently on a sole base. The twins as an independent force can act with impunity operating from Brest and agressively hunt down merchants if they need, the Homefleet doesn´t have the assets to deal with all possibilities. A single German carrier located somewhere between Cape Cod and Liverpool would have been enough to paralyze shipping between North America and Europe and force the Royal Navy not only to send out massive search forces but would also delay convoi schedule as happened during Krancke´s raid.
It has been mentioned that GZ needs plane guards. On their patrol stations they don´t really need them, during operation Berlin and Rheinübung, the raiders made use of aviable auxilary ships to broaden their search front. Convoi´s aren´t fast enough and the Dithmarschens are relatively fast (22kts) to temporarely accompany a riader on their search. They also helped to fish up Arado-pilots from the twins, Hipper and Scheer in these situations. As long as GZ has an initiative and knows where and when to strike they may use them to serve. If GZ is forced to react