I've floated around all three platforms and still use iOS and Android on a regular basis. Here are my thoughts:
- makes a good wireless modem without drying the battery in 2 hours - Samsung Galaxy S III or the Note II. Since you said the Note II was too big, the SIII would fit the bill right now. the SIII comes with a 2100 mah battery to start with, but nothing 20 bucks on Amazon and a 4400 mah batter can't solve. It does make the phone a bit bigger, but solves the battery issue.
- supports the most common applications, including (gasp!) commercial ones I use, say, to find a good place to chill out with friends in an unknown "barrio" - That's just Android in general. There arn't really exclusive apps that I know of that are stuck on a particular phone. Less you are talking about crapware or bloatware.
- top quality predictive texting (Apple's iPod Touch being the best I tried so far) - Swiftkey is big. I happen to like Smart Keyboard Pro as well.
- supports third-party IMAPS servers, with supports for aliases. Android app called K9 if you don't like the email client that comes with the phone. Not sure about the Alias thing since I've never had a need for it.
- supports standards-based, not Google-based, calendar sync, as well as Mac Address book, ideally locally, or through the cloud. Considering difficulties in easily accessing a wifi network in this city, local sync would be preferable, though not mandatory. - Not sure about this one. I know that exchange sync works well and chances locally. I use Exchange sync with my N4 and my calendar says local even if I don't have signal.
- native eduroam authentication - Any Android Phone.
For your point 7, multi-tasking since ICS, and with JB, have been great. You don't see the battery drain you would with Gingerbread. As for rooting, the SIII has a great developer community behind it. It's super easy to root and ROM if you want to, just be nice in XDA, don't want tick anyone off, and it's easier than you think.