The sources you’ve mentioned are a little before our time, but actually bear directly upon our topics of conversation. Lavery talks about this in Ship of the Line v. I. On page 91 he points out that ships of the 1741 dimensions were completely unsatisfactory and that 80 gun three deckers were to be abandoned completely. Apparently, the improvement came pretty quickly, because he says a few pages later that “the typical ship of the Seven Years War was more weatherly, more stable, and more heavily armed than her predecessors.” (p. 102). Now, I did find the quote that Willis cited on page 121 instead of 122, and Lavery says there:
“A contemporary historian wrote that ‘The British ships of 74 guns, built according to the old principles, in many instances,
when a heavy sea has been running . . . have been unable to fight any of their lower deck guns. . ..’ – though it is difficult
to find an example of this happening during the French Revolutionary War.” (p. 121).
As an aside, I am beginning to wonder how much of the “French ships are better than ours” is similar to the “Soviet equipment is superior to ours” that we used to hear during the Cold War.
So, while everyone is agreeing that the later ships are more stable, Lavery doesn’t put any numbers on this. For that, we have to turn to Boudriot. In volume I, page 32 he explains what all of the stability talk means. It’s a long quote, but he tells us exactly what we’ve been talking about.
A good, stable 74 is not expected to list by more than 6-7 inches (16.2-18.9 cms), when heeled over under the pressure
f full sail and close-hauled, which in a fresh or “manageable” wind should drive the ship along at 14 kms/hour. With the
lower deck 36-pdrs run out on the lee side and the gun crews in position (the guns on the other side being secured
i.e. run in, with the muzzles hard up against the ship’s side, and the gunport lids fastened), the list will increase by a
further 3 inches or 8.1 cms. [italics in original]
Note that he says the guns are secured, but not housed. Boudriot defines housed as, “with a muzzle-lashing made fast to the clamp.” (iv, p. 121). Given the distinction between secured and housed, I think an inference can be drawn that the crew does not do a full housing of the guns before performing a tack.
Coming back to the above quote about stability and heeling, Boudriot has a set of three drawings on page 32-33 that show the conditions described above. In the explanatory text for the drawings, he says that a list of 16.2 to 18.9 cm is only 1 degree 24 minutes, while a list of 24.3 to 26.0 cm is only 1 degree 38 minutes. He does say in the explanation that “it is possible to imagine a situation whereby a ship engaged on both sides might have her lee battery run out ready to fire, while the weather battery is run in to the limit of the breechings for reloading.”
The tube weight of a British 32 pounder is between 54 and 57 hundredweight, so 6048-6384 pounds, approximately. A French 36 weighs 7,450 pounds. Along with the sheer deadweight and only a 1 degree roll, Lavery, in The Arming and Fitting of English Ships of War 1600-1815 describes what he calls a “train tackle.” This is described as, “similar to a gun tackle, except that it was fixed between the gun and a ringbolt near the centre line of the ship. It was used to prevent the gun from running itself out when the ship was heeling.” (p. 141). He does say that when it came into use is uncertain, but by the 1780, three tackles were issued per gun. “Presumably one was to be used as a train tackle if necessary.” (ibid.). Boudriot also mentions train tackles, but apparently the French used two on their 36 pounders by 1780. (Boudriot, ii, p. 169 and Plate XXXIX). However, he says (ii, p. 168) that the train tackles in French service “serve to haul the gun in for loading.” So, presumably they would also serve the same purpose as British train tackles? I’m not sure, but think so.
It seems clear from all this that by the Napoleonic era, ships could tack under normal circumstances without much chance of flooding the gundeck in normal weather. Also, it seems that keeping the guns run out doesn’t present much of a problem, at least according to Boudriot. Now, this still doesn’t answer the question about gun crews being able to shift the piece and whatnot while tacking. To be clear, I don’t think they can. Padfield’s Guns at Sea supports your contention about adjusting the guns (or inability thereof) quite explicitly via this quote from William Hutchinson, describing the aiming system in 1781:
The Captain of the gun is to look by the side sights first, and apply one hand to the bed or coin, and make motions with
the other hand, upwards or downwards, for the men on each side looking at him with handspikes to rise or fall the breech
of the gun…then, looking along the top sights, tap with his hand more or less on the side of the guns, as it requires to be
breeched fore or aft by the men with their crows or handspikes…. (Padfield, p. 95)
They also can’t reload, but we had already agreed on that. So, even though you can’t aim, and can’t reload while in a tack, can the guns be fired? After all the above, I still can’t find anything that definitively says yea or nay. I guess it comes down to whether or not you (the general you, not you specifically) believe that an unadjusted broadside can have any effectiveness. I think it’s possible, but we may have reached a point where no further research can answer the question.