Lets start with the last. If we deal with a GZ of 1941 type it does only have 4 fighters (some more on reserve) Bf-109T. Plus a few Fieseler multirole planes with very doubtful effect (maybe against torpedo bombers only). If we deal with a 42 design GZ we deal with 40 Focke Wulf 190 A4/U fighters and that´s pretty much defense if you ask me (plus Luftwaffe fighter screening, some 20-30 more Bf-109 G2/G6). In case GZ stays in a Fjord it will be sitting duck but also more heavily defended by a lot of AA (including those 2 cm Vierlingsflak), this would be a risky tour, esspeccially for bombers (torpedoattacks in Fjords can be considered as suicide). If GZ is in open waters it will have to defend from torpedo and bomber attacks (the former one dangerous), so lets shift to your next point:
You are correct to name the stability, but this factor even benfits GZ a lot: It has a lower positioned main armor deck, a good (...for a carrier...) beam - height relation and therefor is more stable than their contemporary british or even US counterparts. It´s weide TDS would allow very effective counterflooding measures and torpedo hits just have to pass the TDS first in order to make hits on munition storages, avgas depots and so on. We already discussed this in case of Bismarck, GZ has the same TDS: Only repeated hits may cause such destructions (keep in mind that GZ is not a Wasp class carrier with poor underwater protection). I do not deny that repeated hits may be possible (Prince of Wales, Scharnhorst, Yamato, Musashi all suffered repeated torpedo hits into the same compartimentation of their TDS). A damaged GZ is of little worth, since it will continue to present a thread for the allies alike Tirpitz via "fleet in beeing". And as Tirpitz tell us, the ship recovered two times from heavy damage wihtout any possibility of docking in Norway. This lead to the three TallBoy attacks, because the second one showed damage (which was believed to be repairable by the british but we know that these damages indeed reduced the seakeeping abilities of the ship to almost zero).
And what makes me think that allied submarines cannto catch GZ in the open ocean? Well, at first the difference in speed and endurance: 32 kts travel speed with 35 max. designed, it´s almost impossible to catch the ship with a boat only doing 9 kts for some 6 hours submerged (keep in mind that GZ will be a serious thread to subs also as were CVE to german submarines). Actually You would have a tiny timeframe to act and no possibility to dictate the terms of engagement. Thats the reason why the KM did not suffered losses to Uboats in the open ocean (CL Karlsruhe in 1940 was just exiting a fjord when attacked by subs). The Arctic is also a lot worser for a sub than was the pacific: long days during summer (and german planes patroulling), long nights during winter, bad visibility and enemy destroyers (unlike most of the japanese) with sea search radar...
But there is possibility to strike with subs, british and soviet submarines patroulled the Arctic waters and eventually also attacked KM ships but with very little success (all I can remember are damages like Hipper and Prinz Eugen).