What I've done prior to Europe trips is just get International feature activated with Verizon ahead of time. This was with BlackBerry phones, so given they've been International capable, it was relatively easy as I used the existing SIM. I was careful to only use with voice and SMS.
For My last Asia trip I just used a low end unlocked feature phone and bought a prepaid SIM for a local carrier ahead of time. Given these trips are now all a few years back, I'd try the same as you with the Note 2.