Well, this was an interesting rabbit hole to go down. Turns out introducing a second time dimension isn't entirely new. Kaluza Klein adds a 5th dimension in their theory, but they went with another spacelike dimension. This made the math easier if they made it a closed space (eg a limited number of coordinates) - which in turn makes the 5th dimension this extremely small curved dimension. Why did they not go with a 2nd temporal dimension rather than a 4th spatial? Seems to do with the math, and it gets really hairy there quick.

The story could be rewritten so that dark energy is the energy that spills into the 2nd temporal dimension. Dark matter could emerge there after dark energy cools down. Super large d-stars could then possibly emerge very early on in the universe, without needing celestial d-stars exploding to spread d-matter over the universe (along d-time). I still like the idea of c time and d time, of c speed limits and d speed limits producing different types of matter. I like the idea of dilatons working along d-time (where I'm guessing the obstruction to figuring out gravity is removed in 5 dimensions, and they end up with 2 dimensions, or a flatspace) and gravitons working along c-time.

But to actually show any of this, you'd need a theoretical physicist to resolve the issues with two timelike dimensions in KK theory. Who might be working on this? I don't know. Also, there's a very good chance I've completely misunderstood all of this. But if any of this were true, you'd be able to show it by playing with Kaluza-Klein. That's simply beyond my abilities, so I put this story to rest. I'm still going to read more about it, but imagining anymore solutions to this stuff is just beyond me.