If you want to do the eastern part of the Kii Peninsula, good for you! It is one of my favorite places in all of Japan. However, do yourself a favor and allow three nights if you want to go to Ise and also hike either Magose or Matsumoto passes. And even then, you will be very hard-pressed to fit Nachi Taisha in. With only two nights I would drop either Ise or Nachi Taisha. Just my own two cents' worth. Also, have some contingency plans for rain. (It tends to rain a lot there, and there are fewer options for things to do in bad weather than there are in most other places.) And figure out in advance exactly what you plan to do with your luggage. Plan everything (transit, meals, luggage management) in detail and still be prepared for a few hitches. A feasible, nice three-night itinerary is a circuit of the peninsula starting out (early) in Nagoya, with one night in Ise, one night around Owase, and one night in Kii-Katsuura or Shirahama, then ending up in Osaka. Ordinarily I do not advocate changing hotels every night, but if you want to get the most out of that region in a short period of time, you almost have to. (Tip: Don't settle for quick and easy choices on accommodations or try to get the cheapest places you can find. There are some really fabulous places to stay around there. Terrific onsens and outrageously good seafood are available if you look for them. Another strategy for this region is to find a marvelous ryokan and hole up there for a couple of nights, fitting in hikes or a little sightseeing on the arrival day, the second day, and possibly the third day.)
I also tend to think you are maybe trying to fit too much into your trip. If it were me, I would probably cut out some places. For what it's worth, Hakone seems to be a place that many people love to hate these days (of course, Kyoto is on that list too! ha-ha). Last time I went there it was not crowded, and I had a splendid time, but that was a few years ago, and I didn't try to do the typical "round course" or expect Mt. Fuji views.
When I plan my trips to Japan I usually start out with a fairly long list of places I want to go, and then when I really think about the nitty-gritty details (transit, accommodations including outrageous upcharges or overcrowded conditions in certain places on weekends, luggage management, etc.) I tend to pare the list back.
A number of places on your list could be done as day trips from a home base in Tokyo or western Japan. Okayama is good for that.
I wouldn't necessarily cut out Nagasaki, although many people will tell you it won't work the way you have it planned. (On the other hand, I would cut out "Rabbit Island." But that's just me. Just be sure you really know what you're getting. I have seen some people be disappointed, and others be absolutely delighted.)
Finally, remember to enjoy your transit and not just see it as a necessary evil. I feel sorry for those people who spend every minute of their train rides in Japan resenting the time it takes and just wishing they could get where they are going faster. Note: if you plan to take a lot of train rides, a green rail pass can be a super-nice indulgence if your budget can gracefully allow it.