It appears that I have to proactively select the timezone I'm in to Google Drive so that they display correctly. Is there a way I can push this setting to all users within the organization?
You can change your timezone in the settings for Google Drive. See below screenshots.
As for changing it for all users this is not possible. Each user will have to set their timezone individually.
At this time it's not possible to set a default timezone Google Drive and Docs Editors. A workaround is to create create a new spreasheet, set spreasheet settings as desired and use it as a template.
The G Suite admin could set a default timezone for user of a G Suite domain but this is only for Gmail, Google Calendar and other services but not for Google Drive and the Docs Editors. At this they don't have a global setting for the timezone.
Regarding the use of template, it's worth to say that On november 2016 Google launched a new template gallery for G Suite accounts. For details see Create a file from a template.
- Set a time zone for new users - G Suit Administrators Help
- How to set default locale settings for Google Drive spreadsheets (A thread of the official Google Docs Editors Help Forum)
- Save time with new custom templates in Docs, Sheets, Slides and Forms (Official Google blog)