However I'm assuming that Daniel at least continues to move around in time since we see him at the discovery of the chamber at the very beginning of the season, and he also tried to warn child Charlotte not to come back, and the latter had to happen 'after' Charlotte died (in his timeline, that is).

Not necessarily. We don't know what time zone Locke's team are actually in when he turns the wheel. All we know is that the well is now gone, which can actually tie in quite well with the excavation we see in the opening sequence of the season. Daniel may very well be in the "native" time zone for Daniel to infiltrate the Orchid construction site and warn a childhood Charlotte to get off the island.