I think you're missing the point of where I'm going with this.
A phase space, or configuration space, doesn't have to imply anything about time being presumed simply to conceive of that space. It's just a spatial representation of all the different possible states that a system could be in.
A span across such a phase space is thus a pattern of change: the system moving from one state to another through a succession of intermediate states. This is still before we have constructed any notion of time, just a span of possibilities, without any particular directionality to them; we could, so far as we've conceived thus far, scrub back and forth across that pattern of changes willy-nilly.
Time is most generally a measure of changes in the universe, so a span of time is a span of some sort like that, through the phase space of the universe, with every possible point in that phase space representing some possible state of the universe.
But time as we normally conceive of it is directional, so not just any span of the phase space counts as a span of time as we normally conceive of it. A universe at maximal entropy, for instance, may find itself wandering around through a bunch of possible states in no particular pattern, sometimes even repeating the same state, but we wouldn't normally describe that as time running forward and backward in time in such a universe. Rather, time has effectively stopped in such a universe: all those different maximally-entropic states are "the same time", because they're all the same distance along the direction through the phase space in which we reckon time to point: the direction from less entropic states to more entropic states.
The phase space of the universe being more entropic in one direction and less entropic in another is an anisometry: it's not the same in both directions. But the phase space is not globally more entropic in one direction and less entropic in another, so that anisometry is only local. You could look along the less-entropic ("past") direction until you hit a local entropic minimum, and then if you keep looking further in that same direction, you'll see entropy going up again, so locally (in the phase space) that direction is now "the future", even though it's the same direction that elsewhere (in the phase space) it's "the past". That local entropic minimum is "the beginning of time" from the perspective of states on either side of it.
We reckon less-entropic states as "past" and more-entropic states as "future" because memory-formation, like all processes, necessitates an increase in entropy, so the states of the universe that we remember are necessarily less entropic than the current state of the universe, and as we project patterns in those memories beyond the present, we construct an idea of the future.
There are necessarily more high-entropy states than low-entropy states though, so for every point in the phase space, more adjacent points are "immediate possible futures" than are "immediate possible pasts". Because of this asymmetry, possible pasts converge, while possible futures diverge. The further into the past you look, the more determined the universe at that time is. I.e. there are fewer possible states of the universe connected to the present state of the universe through incremental steps through the phase space toward less-entropic states, the more steps you take in that direction. In the limit, there is only one local entropic minimum, one beginning of time. But the further into the future you look, the less determined the universe at that time is. I.e. there are more possible states of the universe connected to the present state of the universe through incremental steps through the phase space toward more-entropic states, the more steps you take in that direction. In the limit that direction, you get the heat death of the universe, the "end of time" even though it's not the end of change, because all change is now inconsequential and directionless, no state of the universe is a possible future, they're all either equally present or else past.
(Oh and as for the "possible worlds" bit, that's because I consider this a form of modal realism, but with possible worlds more like Kripke's than like Lewis'. Lewis' "possible worlds" are more like time-lines in this model, while Kripke's possible worlds are more like possible configurations of the universe, points in the phase space, in this model. "Accessible possible worlds", in Kripke's terminology, are basically synonymous with "futures" in this model; other non-accessible possible worlds are either pasts relative to the actual present, or else counterfactual, "alternate timelines".)
FWIW, this isn't at all contradictory with "time is what a clock measures". A clock is just a system that undergoes routine, patterned changes, which is excellent for measuring distances across a configuration space, just like a ruler with its routine, patterned markings is excellent for measuring distances in ordinary space.