Alright, had to make dinner for the kid.
To make the Blood Spirits work in the IS, or really to advance the Clan at all is to fridge Khan Schmitt and the Loremaster. Schmitt is at best delusional and at worst, incompetent but the one that really screws up the Clan is the Loremaster (his name escapes me atm), and he's the one who convinced Schmitt to jump in against the Burrocks and Star Adders during the Burrock Absorption so he's definitely the enabler of soon to be bad ideas. She's dumb coz she listens to him and he's dumber because well, he killed his Clan in the end.
So assuming you have someone less to jump into doing stupid things, we're off to a much better start already. The other is to accept that there is no chance at all of your Clan becoming the IlClan so don't stick you neck out and to do stupid things to achieve that. Essentially the Blood Spirits have to make the decision that the Ghost Bears did and aim for what's achievable and not what is a fairy tale. And that's going to be really hard for the Blood Spirits because as a Clan, they have these blinders to what the reality is compared to what they want it to be but, with a sure hand they could avoid that pitfall for the most part.
I firmly dispute any chance, at least until after Tukayyid that the Blood Spirits would do any better than the Nova Cats. Nova Cats had a much larger, and better equipped Touman. The Blood Spirits aren't total garbage but they're overall allot less flexible and allot more parity with IS forces. Yes they have tanks, but most of what they have are not GOOD tanks and have nowhere near the industrial capacity bigger Clans have. They are truly Clan second fiddle out of the Invaders. So they're not going to take as much territory so what they do take is firmly held. Don't mistake their "bigger" Clusters or their greater number of them as being good - they're okay, but the vees are no replacement for the mechs other Clans use, at least with the way they use them. They're going to a thinner ribbon, more in the style of the original Ghost Bear corridor than the broad corridors of the Wolves or Smoke Jaguars. They're also going to have different disputes with the Smoke Jaguars than the Nova Cats did amd I'm not sure the Blood Spirits could deal with those challenges easily.
As to inviting the Fire Mandrills along, that carries allot of risk. You'd have to do it in the style Vlad did with the Hell's Horses to make it feasible and not show that you're weak. Remember the Invader-Homeworld Clan dynamic means the Invaders basically have hold themselves aloof from the Homeworlders who end up resenting the hell out of it. The Fire Mandrills other problem is well... they're Fire Mandrills and basically you're trying to herd a very dysfunctional Clan into an already pressure cooker of environment. No Telling what those guys will do! I honestly think the Blood Spirits are in a hell of a spot as an Invader clan. There are better pairings and partnerships to be had than the Fire Mandrills.
Lastly, there's the Burrock Absorption. I do not believe it'd go as cheerily as it did in canon between the Burrocks and the Star Adders at the time because the Blood Spirits, no matter how outraged they are, just would not be in a position to interfere and that allowed the two other Clans to focus on the Blood Spirits, shattering them and in a way preserving themselves as by the end of it, they had fought with honor and aligned at least briefly, politically in the aftermath. I think the Star Adders would have had a much tougher row to hoe, maybe not taking as much concentrated damage as they did but spread over the Clan as a whole, leaving them in a longer period of downtime. Maybe the Burrocks prevail and survive but it still leave them unable to bully the Blood Spirits who use this time to build themselves up.
There's more thoughts to be had, but that's for another post.
