Sadly, there isn't really any use for self-estrus with pursuit. Once upon a time, Breastfeeding was affected by pursuit when paired with Welcoming Invitation, leading to some crazy healing... but that's a thing of the past now.
That said, we have some options. I'm busy at the moment, so you'll forgive me if this is off the top of my head instead of properly researched...
...There are two big options: Devil's Bargain (Pursuit 2 to your side of the field, inflict Lust Mark at the start of your turn) and Synchronized Cycles (select squeezer on your side of the field, select opponent's squeezer, former force-squeezes, latter gets Estrus).
The former pretty much has to be combined with Iron Will on all your squeezers (from Clearing Mind, Purity Field, or being SoWaD/Partnered Nun), while the latter wants to be combined with Blood Moon for the Pursuit (Force-Squeeze gets +1 Pursuit for all squeezers).
I can't build decks right at this moment, I'm busy, but the keys are Insincere Gift to give a copy of Devil's Bargain to your opponent so their field self-destructs, and... double summon to have more squeezers then your opponent so you can shut them down with Synchro Cycles?
-I'm less busy now. Behold, Cult Mechanicum.
It's... okay. You could and probably should drop the Synchro Cycles for something else, but it loses a lot of its identity doing that.