Thanks!
You are correct about the impact of the Barracks Emperors.
However, on subsequent reading, I must correct my last message to admit that there is a GURPS JTAS article (15 Apr 2003) describing how Solomani worlds that remained independent of the Imperium continued, even expanded, their colonisation efforts "rimward and spinward" during the 600's. So maybe expansion past Near Bootes started a bit earlier than I thought.
Reviewing the likely 3I borders in c.600, compared to c.1107, it seems as though in c.600 the 3I had greater penetration into Alpha Crucis (per MgT: Alpha Crucis), but less penetration into the spinward portion of the Rim and Magyar. Hence the 3I was on the "frontier of settlement" in Alpha Crucis (ie. no interstellar states of note remained independent, only an assortment of single worlds). However, in Magyar and the Rim, there _did_ remain a significant number of powerful independent smaller states that could support large-scale colonisation efforts. (Probably another "build up our strength _away_ from the big bad competitor" situation.)