You know, strangely enough, I can see some modified ocean going ship, say a 12 X 14" BB with the same engines as the Ocean going ship, just with so much extra armor that it barely floats. Say 50% thicker main belt. And I can also see one sinking in peace time and killing 1000+ sailors.
Cold freshwater won't float as much as salt water will. Something like the
Tegetthoff-class, with an 8" secondary battery and a 12" belt and deck, but with a generally sturdy and buoyant hull. These ships don't need to be handsome,
I used to live in Buffalo, so I can easily see 10" to 16" guns on both sides of the lake attacking each other. I am pretty sure a standard 15" guns shoots across the widest part of lake Eire or Ontario.
Yeah. But even the 16"/50 caliber M1919 couldn't range across the entirety of Erie or Ontario, maxing out at 42km with their systems as built. You could maybe squeeze 50km out of them with everything, but that means pretty much everything valuable is well in range of coastal artillery batteries. Everyone would be on edge all the time.
Now the truth is that this makes for an unstable situation, and almost guarantees a USA/UK war. IMO, it also means the USA enters the alliance system opposite of the UK. If I had to bet with limited butterflies, we see the France/USA/Russia v. UK/Germany/AH alliance. It would make a great TL if one went to the details to write the good 20 year build up before the war. It is likely the weaker side still spends enough to make sure it still is a long war. I have pictures of a huge USA main battle fleet, and several armies of South Asian soldiers in Canada.
Oh yeah. This would be a very big deal, and would make everyone very nervous. It'd completely alter the balance of power worldwide, and would make the Anglo-Japanese Alliance all the more important, while France would likely expect American reinforcement and the protection of French colonies in the Caribbean and Pacific. So we're talking about a much larger USN overall, with more focus on opperations further out, so you'd have two strains of Battleship designs, with Lakes designs, and designs suitable for long range missions, like OTL USN Doctrine called for.
That the Salish sea would likely be impassable during wartime would likely also be seriously problematic as well (well, the Canadians could move ships in and out by Queen Charlotte Strait, heading south to Vancouver but that's rather tricky.) So the UK would vastly be even more dependent on the IJN in the Pacific, using Yokosuka and Kawjalein Atol as major bases, since they don't have any secure harbors in the eastern Pacific. Unless the UK grabs Hawaii, (possibly as an "ally", possibly as an outright colony.)