How would the leagues starting in October allow them to end in May?
Is your supposed "solution" the idea that instead of trying to get as many players as possible to participate, you have the European leagues also go on while the World Championship is underway, thus having even less?
I really don't understand what you are trying to say here.
a) the European leagues all start in September and are finished at the end of April
b) the NHL already starts in October, and it usually isn't finished until late May / early June
c) the tournament starts when round 2 of the NHL-playoffs is more than half-way finished
I don't see how your change improves anything at all.
As for your favorite idea: absolutely not. Preseason is the worst time to hold a tournament. It makes a mockery out of it. Players are completely out of playing-shape. Having two groups, one of which always plays in North America doesn't sound like a good idea either, nor does hosting a final four. It's stupid enough that they allow two countries to host at the same time. It takes away all the fun of hosting the tournament. Up until they came up with this stupid idea when Sweden and Finland shared the tournament twice, having your country host the World Championship was an event among the hockey fanbase. Sharing it takes away the fun of being the host.
Beyond that, NHL-teams sure would love to not being able to get their players to learn their system, 3-4 pre-season games are not nearly enough to get a good look at anything.