To be clear, my conception of a "universal ordering" doesn't mean we can always measure when things happen relative to one another. If two things are causally related, we know one happened first. If a tree falls on Andromeda "right now," I don't know if that happened before or after a particular timestamp here on Earth, but it either did or it didn't. (Same goes for all possible timestamps for all clocks going at whatever speed they are going; their timestamps will diverge, but they could still be ordered if we knew the speed they travel relative to light and the starting value and how often they tick, e.g. once per second nanosecond or whatever. So if we had an observer on Andromeda with such a clock, we could eventually order events there relative to events on Earth based on the timestamp they report, though it would take a very long time for their report to reach Earth).
Are you sure that's not compatible with special relativity? Genuinely asking. If not, is it possible to explain why it isn't? I'd like to know (but if I'm asking you to write a book, never mind).
When you say you're in the Rovelli and loop quantum gravity camp - is that compatible with special relativity? I'm guessing yes, but let me know.
I think time is an emergent property of causality. That sounds close to what you are saying (possibly a different way to say the same thing).