I don't see this as a good idea. The shorter a campaign season is, the easier it is for a politician to B.S. his/her way into elected office. I've heard that Australia's campaign season is only a month long; if this is true, this would be a horrible model for the U.S., since Trump would already be president.
The only reason why long election seasons seem terrible, is because they are media circuses. If campaigns were about mature discussion and ideas rather than mudslinging and empty, pretentious rhetoric, no one would mind the length of a presidential season. We're only sick of it because of the endless, infantile stupidity of it all.