ok, here's the thing - even if you are not sure when the new month started - because the moon was too thin/narrow/hard to see/cloudy, when it comes to the middle of the month, it is easier to see (when the night is clear) when the moon is full.

So why is that not used as a "secondary measurement" to make sure you started the month at the right time?

Yes there is a hadith about when to start the month and if in doubt have 30 days, but that hadith does not account for when some people have 29, others 30. Would this not be a good time to calibrate any disagreements?

Only saying this because while many have 15 of Sha'ban tomorrow, the moon was full last night.