No personal experience with "instant" rtw issues (so I should probably save the bandwidth for someone else!) but from reading previous comments, it would seem that if you were sitting there anxious to fly away, the tariffs people would accommodate you within a couple of hours. Just be careful not to include anything controversial in your itin - if you have grand ideas, you can request a reissue and debate them at your leisure later, for USD125 or so.

Reissues, more or less the same process (perhaps even more complicated because history must be subtracted) tend to work that way - they'll generally be coordinated with the rate desk and handed to you fairly quickly.

Of course pick your flights (verify availability) ahead of time and book them before heading to NRT.