What are the best practices and tips for effective communication for a 4-5 month cross-functional project?

The first is to have a common objective. Then clarify the roles and put rules of engagement. Everyone must buy into their communication plan and give the realistic timelines for the milestone deliveries. 

Make it intentional by documenting it, putting it the project plan, adding it to your calendars, and defining who owns it in all it's different forms.
Leaving it informal is the way it gets forgotten, missed, ignored, and deprioritized after a long week.

Ensure you take exceptional meeting and project notes I found that the more cross functional the project (more diverse and numerous teams) the harder it is to get all participants together interactively even with Teams/Skype/WebEx/Zoom. Those notes and presentations need to do an amazing job of communicating expectations, updates and where you need help from each team and individual to be successful