The problem is not whether or not the Fi-167A could take off in these conditions (we don´t know), the question is why do You consider the SWORDFISH beeing better suited?
Ark Royal was able to launch her Swordfish under pretty harsh conditions because of the slow speed and easy lift off of the Swordfish from her deck, I'm not sure if the Germans, who were very modernised would have even dreamt of having such antiquated (in their view) aircraft.
But as mentioned above, the Fi-167 is STOL (=short-take-off-landing) and requires much less speed
to take off in any given load condition than the Swordfish (or any other carrier airplane of ww2). At the carriers max. speed these planes can virtually lift off vertically. In addition to that, the Fi-167 had better power-on controll
characteristics in the difficult approach regime.
That beeing said, the conditions for take off from ARK ROYAL in the decisive attack were very difficult, almost to difficult for carrier operations:
'I was on HMS Ark Royal and the captain didn't want us to go, but in the end he turned into the wind and dropped the speed to five knots.
'The ship was pitching 60 feet, water was running over the decks and the wind was blowing at 70 or 80mph.
Thus, Ark Royal was taking a high risk to launch these planes in these conditions, it was way distant from something which may be claimed regular "flight operations".
Then, You mention that:
I still maintain that his theoetical 35 knots would have been attained under test conditions and may not have been always achievable under North Atlantic conditions given the size and windage area of such a ship, wereas a KGV or Renown could probably maintain enough speed to catch and sink her because of their much heavier construction.
I don´t think Your explenation matches the findings of the germans, who conducted exhaustive windtunnel studies with the ships in question:
According to their findings, windage effects are less pronounced in GZ than in cruisers of the HIPPER class due to their many portrudes (turrets, superstructures) and they really invested a lot of effort in figuring out the best concepts at different conditions. You seem to propose that a 50 kts wind reduced GZ speed by 10 kts while that of a RENOWN or KGV is not or only slightly impaired, allowing them to catch GZ. I have to respond that no- this is not the case.
You mentioned that raiders were not primarely responsible for inflicting losses of RN warships, and to that I agree. That´s not their purpose. In defense for the RN home fleet You mentioend that losses were occurring not only in the Atlantic. That´s true, too. But it´s a war of attrition in a sense and in the period in question, the RN is overstretched over the different theatres and doesn´t have enough naval assets to deal with everything:
[+]escorting priority convois with battleships and DD
[+]escorting convois with DD for ASW
[+]providing an answer for the Fw-200 long range bomber meanace
[+]providing presence in the indian ocean
[+]providing presence in the menditerranean
[+]patrolling DS, faroer strait and other areas
[+]protect the shores and channel from E-boats, raids and submarines
[+]have enough residual units remaining to serve as home fleet backup
[+]provide taks forces to hunt down auxilary cruisers and raiders
[+]provide task forces for coastal bombardement / defense
Whether or not losses occur in the med, the far east or the North Atlantic is insignificant. You can´t magically create units already in use elsewhere and You have to compensate for losses or face degradation of power in these theatres. A raid in the North Atlantic in this period would very significantly impact force balance in the mediterranean, f.e. After the loss of ARK ROYAL, you need Malta been resupplied with aircrafts, or do You use the carrier instead to help VICTORIOUS hunting GZ in the north Atlantic as AR helped VICTORIOUS against BISMARCK? The answers to these questions bear consequences...
You also mentioned speed as an questionable asset. But the comparison You drew between SUFFOLK and BISMARCK is misleading. First of all, SUFFOLK was nominally faster than BISMARCK and not slower (design speed advantage of 2.5 kts, in action bismarck was faster and Suffolk slower, resulting in negliable speed differences compared to all other navigational factors) and second SUFFOLK indeed lost contact twice to BISMARCK. Once after sighting temporarely for some hours (the principal reason for Holland beeing misplaced in the morning of the battle) and then after breaking with PE.
Here You compare a cruiser which is nominally slower
than GZ. Unlike BISMARCK, GZ is indeed able
to break contact by throtteling up to top speed. GZ by measure of it´s design speed is 6 kn faster than the BISMARCK-class and 3kts faster than the SCHARNHORST-class. It´s natural speed is higher, too as is it´s cruise speed.
Thus I feel confident to hold my opinion that it won´t be possible for aviable RN units to track her. Some may make contact (sighting or radar contact reports) but to track her as has been seen during operation Rheinübung by Suffolk and Norfolk is virtually impossible, You need to slow her down appreciably before achieving this. But when You can´t track her, how are You going to fix GZ future positions for airstrikes supposed to hit her?
They are plenty fast enough to cut her off if they are in front of her as you suggest Rodney was. Of course if this is occuring instead of the Bismarck sortie you forgot to mention Hood and POW.
In this situation, after running 32 kts instead of 28 in the previous night, and without SUFFOLK and NORFOLK been able to track, this engagement doesn´t take place, GZ stands 50nm further to the southwest than BISMARCK at dawn -HOOD and PoW (or KGV and RENOWN for that matter) are unable to make contact. Distance would be 70nm between the forces and increasing. It´s very unlikely that the RN have a fix on GZ´s position this time and likely that they direct their forces to less optimal search areas. There would also be a lot of wrong sighting reports from ships referring to single engined biplane carrier planes, which may refer either to the Swordfishs operating from VICTORIOUS or to Fi-167 operating from GZ (the latter also is a biplane, unfortunately, making ID kind of tricky).
Sachsenwald rescued two survivors according to her report. That´s also what Your reference gives. There are a number of ships send out durign operation Rheinübung conducting supply and beeing lost but again, that didn´t destroyed the logistic ring or impaired the operational logistic base to conduct later operations, such as the planned outbreak of mid 1941 with TIRPITZ and SCHEER or that with TIRPITZ and HIPPER had Hitler agreed upon this. There are plenty of supply ships aviable to support GZ in the North, Mid- and South Atlantic in late 1941.