The past guidance that has been given to me by multiple agents in the past was that if I had a significant schedule change (30 minutes or nonstop going to connection, as defined by UA), I could rebook within the +/- 7 day window and preserve the upgrade. Basically rebooking within +/- 7 days without add-collect is considered an invol rebook, which also comes with upgrade preservation. Any rebooking outside this window would be considered voluntary, and thus trigger both add-collect and loss of upgrade.

I won't go into details, but my conversations last night, especially with the supervisors, lead me to believe that there isn't/was never a clear-cut policy for preserving upgrades on schedule changes, which explains why some agents/supervisors have a much easier time doing this than others. With enough perseverance, I've always managed to get my desired set of flights, including twice this year (changing dates by five and four days, respectively), but it's never taken me this long and I've never encountered so many agents and supervisors in a row who were so adamant in their ways.

In this specific case, my original LAX-HND flight was at 12:45pm. The latest LAX-TYO UA flight available on the same day now leaves at 10:50am (the nonstop to NRT), and they had rebooked me onto an even earlier departure, leaving at 8:15am and connecting in SFO. Neither of those times worked for me. I asked to move the outbound six days earlier and the return two days earlier.