Time is real, so I'm not a fan of timelessness.

The point of timelessness is not to say that time is unreal, merely that it is superfluous.

It's difficult for me to follow your comment. While I'm familiar with the theories you discuss (with the exception of string theory and quantum cosmology), I don't see how some of them are linked to this. I'm not trying to do anything so great as unify quantum mechanics and general relativity.

As soon as mathematics represents a history as a "trajectory" in a state space, it is already becoming a little "timeless" in a formal sense.

Yes.

Consider something as simple as a time series. You can plot it on a graph and now it's a shape rather than a process. You can specify its properties in a timeless geometrical fashion, even though one of the directions on the graph represents time. In talking about flows on state spaces, I don't think you're doing more than this.

Time is no longer "one of the directions on the graph". If you fix a trajectory, then it comes with it's own time, but the more interesting object is the flow, which does not have any sense of time.

We agree that whatever I'm doing is mostly harmless.

So what you're doing is harmless, from the perspective of a time-realist like myself, but it also doesn't really embody the full revolution of Julian Barbour's ontological timelessness, which necessarily involves both general relativity and quantum mechanics.

That will have to wait for someone else. I haven't read Barbour, and it sounds horrifically difficult.

But for nonrelativistic systems, it looks like formal timelessness in a causal model (in the sense you describe) is just a change of perspective that's always available and can always be reversed.

Probably. But such a thing could still be worthwhile.