We have the technology to actually quantify this now!
It looks like Wraithbound is the only rare pet prefix that the Bloodsworn Signet can roll, and for sufffixes we have of the Wild, of the Untamed, and of Caged Souls. If we’re OK with any combination of these, we have a 0.34% chance for a ring with two pet affixes. And Karroz drops 1.3 rings per kill. That gives us 156 expected kills to get such a ring. That’s a almost 4 hours of farming per ring, if it takes 1.5 minutes per kill.
Of course, the flip side of this is that people using GDStash to test builds can and do still aim for somewhat realistic-to-farm MIs (with varying degrees of success), using my spreadsheet.