Also, note that some projects with multiple phases are already using numbers on the badge for a different purpose - the phase number associated with that badge.

I would like to see new badges for at least 5 and 10 years, but I would settle for a new project. It would be nice to have a new goal.

Well, 4, 8, and 16 years would be the natural next levels (= double the prior badge's contribution). Next one after that would be 32 years, although I wonder how many "natural person" grade crunchers (as in "crunchers other than college/commercial system operators") have actually managed to run a project to 32 years.
There is also the option of switching from the currently square shaped badges to say, hex shapes. If we would now start the existing color scheme *again* (bronze hex = 4 years), we have an instant solution covering contributions up to 128 years.
If you do the hex shape by essentially "cutting off" the appropriate sections from the colored back ground (i.e., you let the skeeter legs or the "2" stick out over the "rim" for the hexagon), you don't even need to do a lot of thinking about making the project logo "fit".
Add an Octagon for the next level and it gets you to 8000 years.
May I propose to honor crunchers with contributions exceeding 16000 years for an individual project (i.e., the hypothetically next badge) with a virtual personalized "plaque" instead ...

This ground has been covered before, indeed. While I can in no way compete with the power crunchers in (future) badge levels, I can be proud on my full set on the left.

I do what I can with my available processors, and to me, this is what I'm proud of. Not the level compared with others, but the level achieved with what I can contribute.

This doesn't take away that in the 2-4-8-16-32-and-so-on I would have a 16 now and wouldn't mind to show that one here.