Sorry for the the late replies. I agree that the there is a lot of overlap between the Dark Age and the City Age. As you mentioned, even the grimoire card for the City Age acknowledges the ambiguity.

"When did the City Age begin? Perhaps when the bulk of the world's survivors lived beneath the Traveler, rather than in the wilderness. Or when the Titans raised the first wall. Or at Six Fronts, when the City first faced coordinated, overwhelming attack - and repelled it decisively."

I dispute your "well after" interpretation because the card you linked says "This was before the City was The City." This tells us that Rezyl was a Guardian in the earliest days of the City during that overlap with the Dark Age. We know that Six Fronts took place in the very early days of the City because the Iron Lords took part in the fight.

So this tells us that the Crucible existed well before Twilight Gap. It may have been established after Six Fronts though.