Well, a good part of my reluctance also comes from the fact that you're basically saying the entire Minotaurs chapter is getting redirected to attack you, breaking off whatever else the Inquisition had it doing out of the million+ worlds of the Imperium, because you made them a bit pissy. Which is pretty easy to do, actually. And beating them would be extremely hard, especially when you consider we have six Imperial Fleets to worry about in such a scenario too. It just seems unnecessary, since if the Inquisition declares Excommunicatus Traitorus, everything starts going to shit anyway. I feel like it would be better if they came only if you'd managed to stick around for a while as an thorn in their side without being blown to shit or blowing the sector all to shit; basically, once the Inquisition has the need and the time to call them in. Or, as another possibility, if you've been naughty but not too naughty, they function as a slap on the wrist via powerfist and attack one place you own with a small strike force; basically the Inquisition trying to knock you down a peg and show you who's really in charge. And there is an element of risk to fighting that force; if you kill enough of them(and in this case the battle would by necessity be a time-limit affair), and I do mean kill, not wound, so their Apothecaries and whatnot surviving would play a factor, they get pissed and send the whole chapter after you for vengeance.
Disclaimer: I know very little of the Minotaurs, I may be butchering their lore. My apologies.