Well, the fastest way is to assassinate all your male children but one.
Make all your other sons bishops.
Okay, guys. My fault for asking about the fastest!
Suppose I just want to limit myself to adjusting the succession law. I suppose I don't really need primo everywhere, if anything, one of the kingdoms being gavelkind shouldn't pose a problem when others are primo (duchies will be split but the kingdom title itself will go to the oldest without regard to the oldest son already getting everything in other kingdoms under primo).
And another question:
I have a guy whom I betroth and marry to the sure heiress of two counties (old father in prison, she's in my court, so is my grandson her groom). I believe that if I manage to grant him a duchy in time, then even if his wife dies first, then their heir, being a count under my enemy (an independent superduke), will switch to my allegiance and will not somehow forgo the duchy on account of high authority? (I am actually the de iure king of that heiress's counties and of the duchy I'd grant to my grandson, each lying in two separate kingdoms held by me. I may have to introduce high authority to switch to primo. This could, ironically, make my de iure vassal counts unable to pass out of the realm of my enemy the superduke who holds their liege duchy.) I would assume this scheme to be fail-safe but I'd rather be 100% certain because I'm running out of duchies.
I am Emporer of Britannia, and holder of several King-titles including Denmark and Navarre. All are on Primogeniture succession, but Denmark and Navarre are agnatic-cognatic, while the others are strictly agnatic. I've got a daugther, the next male heir is my cousin.
My guess is because Denmark and Navarre are not in the de iure Empire of Brittannia. It's generally hard for kings to become vassals of emperors unless the kingdom is in the de iure empire.
If the cousin is unmarried or has an unmarried heir you could try and get the guy married to your daughter. Or you could employ some other shenanigan to make sure a marriage of heirs eventually takes place (no matter that a 30 years old princess will be marrying a 16 year old boy for instance, dire needs require dire solutions).
Or you could switch the empire to agnatic-cognatic. The cousin with his kingdoms within the empire would become the vassal of your daughter, I believe. You could marry the daughter to someone from your dynasty (or matrilineally to anybody), then wait for an opportunity to arrange a marriage of heirs.