How do Buddhist monks deal with meals while traveling across different time zones?
"Should any bhikkhu chew or consume staple or non- staple food at the wrong time, it is [an offence of Confession.]" (Paac. 37; BMC p.362). Here the 'wrong time' is defined to be from noon until dawn the following day.
So regardless of which timezone a monk is in, he can consume food between dawn and noon. All you need to check is where the sun is.
It's not possible to have such problems when keeping Vinaya and abstain from using Yanas (vehicles, burden others with their traveling in not suitable ways), so the question is actually not proper but a result of wrong conduct at first place already. See also Pāṭimokkha for 21st century
When slight things are made wrong, it grows larger and larger and becomes pointless.