Thinking about it, I have a couple of other interlocked theories as to the identity of the Minnesota tribe, and I make no claim to originality as these have probably been thought about before:
1. The Lyrans working alone: That the effects of the Minnesota Tribe's raids (almost exclusively on Kurita soil) worked to draw a good amount of the Dragon's forces to their Periphery border can't be an accident. it would not be out of the realm of possibility that Archon Jennifer had LOKI scrape together the cream of their Star-league Spec equipment, painted them with the livery of a known unit and sent them off with the appearance of coming from the Deep Periphery.
Pros to the theory: Again, that the most direct benefit of the affair was to the LCAF (the old question, "cui bono?"), and that they would have had means to do it. Logistically, it would have been simpler for the Commonwealth to get to the Periphery border undetected than anyone else.
Cons: I'm not sure if LOKI had operatives loyal/fanatical enough to commit suicide to keep the kayfabe going, or to go way out into the Deep Periphery to fool a ComStar survey party. If it was found out, it would mean automatic war between the LC and DC (and a quote about "sleeping giants" could come into play), and a diplomatic black eye to the Lyrans.
2. ComStar stirring the pot: We know that ComStar was very willing to keep the Successor States at each others' throats, and what better way to make sure that happened then to force one to expose their throat to another? ComStar had hidden caches of Star-League equipment, and archives on the SLDF and so would have been in a prime position to spoof a SLDF remnant attack.
Pros: Means, motive and opportunity. they would have had operatives loyal enough to commit suicide, and we have only the Explorer Corps' word for how far they tracked the Tribe's trail. it would have been ludicrously easy for the highest levels of ComStar to have faked that or just flat-out lied about it.
Cons: Possibly too many moving parts -- SOMEONE would have had to have noticed ComStar moving numbers of military-grade Dropships and Jumpships to the Periphery border, at a time that ComStar could still ill afford to be caught out as a military power in their own right. If found out, would Jinjiro have stood for it, even though retaliation could have meant an interdict? Or would he have tried to seize every HPG he could?
3. ComStar and the Commonwealth working together: Not directly, as ComStar wouldn't want to risk exposing themselves to anyone yet, but through several intermediaries -- say a Star League staybehind or Mercenary unit who "just happened" to offer their services to the Commonwealth for the scheme. That would possibly negate the "hmmm... why is the phone company moving a sizable amount of heavy military equipment through Lyran space?" questions.
Pros: The best of both worlds -- both ComStar and the Commonwealth have plausible deniability, ComStar can still lie about having tracked the tribe out to the Deep Periphery.
Cons: At some point the conspiracy becomes so big that it seems implausible that someone wouldn't have talked. There's still the issue of everyone in the raiding parties being so committed to the masquerade that they'd willingly commit suicide for it.
The common thread: In any case, we have to account for the Minnesota/331st logo on the BattleMechs that gave the tribe their name. It's possible (and for the purposes of this theory likely) that the culprits picked the livery of a unit that they knew to have gone on the Exodus with Kerensky without knowing their ultimate fate (there was no way that ComStar or the Lyran Commonwealth could have conceivably known about the NotNamed Clan) and they just happened on one that would centuries down the line spark unintended-at-the-time speculation.
