Wow, Round II like Round I ? German supermen fantasizes apart how to you get that? Are you saying an amphibious assault with no specialized landing ships or doctrine, against a mobilized defender waiting for round II is going to be anything other than a one sided slaughter ( hint the Norwegians are the happy ones ) ? That's not even counting all the ports the British can supply/reinforce through that are out of range of German fighter cover, that mine fields work both ways, that fighting over Norway is just like the BoB in terms of what happens to pilots ( ie German ones are lost, allied get in a new plane ). Its attempting Sealion over an even wider channel. If the KM comes out to play its going to get wiped out very quickly, the Luftwaffe gets depleted even more and Stalin is very happy.I think the problem is that you are assuming Norway round II would be the same as Norway round I.
It won't be for some of the very reason you describe.
But in Round I the British and French forces never entered the Skaggerak apart from submarine pickets - they won't in round II with Denmark and the airbases wherein in German hands
Assuming France goes as per OTL then the British have to decide where to spend their limited manpower. A failed invasion of Norway would give the opportunity to garrison Norway and fly bombers into the heartland of Germany. For this reason the Germans have to go for round II. I question whether sufficient British and CW ground troops will be spared to significantly increase the Norwegian army - if they are positioned then I suspect they will be concentrated in the vital areas for British interests i.e. Narvik and Trondheim.
Germany won't be able to go further North in a successful Round II than Trondheim / Mo I Rana - but this will be sufficient to prevent the RAF from threatening either escorted bombing missions to the heart of Germany or unescorted bombers anywhere they like. Which is sufficient (along with securing the Skaggerak) for Germany.
To recap - I can't see the RN putting its ships in harms way to protect Southern Norway, I can't see the Germans venturing outside of the Skaggerak (so no third battle of Narvik) but I can see a round II where the British and Germans are content to partition Norway as mentioned earlier.
OTL worked due to surprise and the Norwegians trying to be neutral so not letting the Allies in till too late. Things like the propositioned ships in harbors , the effectively unmanned airfields and coastal defenses, lack of radar etc just would not apply second time round. Quisling and his cronies will be out of power or in jail depending on what the POD was so no fifth column disrupting things. First time depended on rolling 6's , second time would need 7's.