What if the Royal Navy totally destroyed the German fleet at Jutland?

Trying to move into the Baltic is, I think, about as likely as using now surplus units of the Grand Fleet to make another attempt to break into the Black Sea.
One of the more interesting facts about WWI is the influence of the press.

To set the scene correctly it is also important to acknowledge that 'democracy' was only starting to be the norm. Parliaments and the voice of the people was not old as institutions. In many instances, I think the start of WWI can be likened to the 'usual' wars: the regents (Kings and those things) were waging wars against each other, but it had hardly anything to do with the 'people (except they had to fight the battles).

The last such war might have been the Franco-Prussian war.

Now, suddenly, schooling is the norm. People can read and write (the amount of letters from WWI were staggering), newspapers and opinions are abundant. The 'Kings' cannot just do things anymore. Checks and balances (even Bismarck had to listen to what the parliament said).

it means that the new normal is for a government to justify what they are doing. Public opinion is now important.

So, as much as the start of WWI might have been the usual, it was not the case in 1916.

If it is correct that the majority of people (and newspapers) would have liked to see peace return, the slaughter has to be justified.

Sure, it was, but what if France, UK and Germany had listened and tried to govern according to the will of the people (at least to avoid a revolution!).

That would have been the incentive to negotiate something that can now be justified in the newspapers.

Just another view on things