Be sure you're working with accurate, complete, information about the legalities. I know nothing about what having a New Zealand passport means in this situation, but you may find you get extra time in a country only in it's your arrival point in the Schengen Zone or the point from which you depart. The UK, Ireland, Turkey, Montenegro and Bosnia-Hercegovina are not currently part of the Schengen Zone, so you may well be safe anyway. But be sure; it's extremely inconvenient and possibly costly to discover you have a problem after you have a pretty firm itinerary and have already bought some of you intra-European transportation.
I agree wholeheartedly that a trip of this length that is overwhelmingly major cities will ultimately be exhausting (mentally as well as physically) and simply not as much fun as a trip covering less geography but a greater variety of sights. Depending on your interests, you need some time doing things like walking/hiking in the Alps or Dolomites, riding a boat down the Rhine, zigzagging across an Italian or Swiss lake, etc.
I'm a traveler who enjoys both museums and just wandering around, enjoying being in a place that feels foreign because of the language, the smells, the food, the architecture, etc. A lot of the best museums and many key historical sights are in the major cities, but the just-being-there thing can be done in smaller, generally less expensive, places. Those spots are often less touristy, too (fewer MacDonalds and Starbucks, typically), which for most of us is a plus.
I spent the entire summer after I graduated from college in Europe (in 1972...), student rail pass in hand. The pass was a lot cheaper then, and intra-European flights were way beyond the pale, cost-wise. I didn't have the money to pay to go inside a bunch of attractions, so I spent less time at my destinations than I did on subsequent trips. Even so, I covered a lot less ground than you have on your list (no Ireland, Scotland, Belgium, Portugal, Croatia, Greece, Turkey, Sweden, Norway, Finland, Estonia or Poland; but I included a 3-week tour of Moscow, Leningrad and Kiev), so you're right that you need to rein it in a bit. I even felt I had to leave out Rome, though I got as close as Florence. And I didn't get to Greece until my third or fourth trip to Europe despite its being probably the place I was most looking forward to; the geography was against it in the days before airline deregulation.
I've been to most of the places on your list (not Ireland, Scandinavia, Belgium, or Estonia) and they are all totally worthwhile. The thing is, for every place on your list, there are many other great destinations in the same country--smaller destinations, cheaper destinations, quite possibly distinctly different from the (mostly) monster cities you list. While you could see a bit of Paris in 4 days/5 nights, it would be shame to spend that little time in the country of France.
None of your points of interest strike me as too much of the same except I'll grant that Kotor (which I did like) is a bit of a mini-Dubrovnik. So I don't think there are quick answers here. What I'd do is think about the 3 to 5 places (could be entire countries) I was super-excited about, research those (single-country guidebooks are 1000% better than someone's guide to the entire continent) to see how much time I'd want there (not just seeing the capital city!), then begin expanding my trip outward. With the availability of inexpensive flights (but beware luggage costs), it wouldn't be irrational with a trip of this length to do something like Greece-Scandinavia-Spain-Portugal if those widely scattered spots are your top priorities. If a major goal is to see a bit of a lot of different counties, you might prefer to look at a trip through the western and central part of the continent.