Can we move, report, and then Invest?

Yes, you can! You won't be able to move after reporting, but you'll still be able to do projects after reporting .

If you encounter any problems please let me know!

(also moved the thread to the campaign-relevant board)

Presumably that would create issues if we moved to a new location, failed to capture it and then spent the project, would the project fail if we didn't secure the location?

The standard projects (and buildings) are all performed (or built) as soon as you click the button, while turn results are calculated at the end of the turn. So no, the project would not fail- it'd be finished by the time the turn results are calculated.

Do keep in mind though, that when you invest in a location, you are essentially giving it a one time boost in health (say, from 50 to 60 or whatever). That effect is not reversed when someone else conquers the location- even if they conquer it on the same turn. Same goes for buildings- if you build something in an area and the area is then captured by someone else, then the building belongs to them now.

Of course you could always just conquer it right back ...