I'll extract some one-liners from your post, Foobar. Thanks for the thoughts.
I certainly would like more information about exactly what all of the techniques involve, as I have very little firsthand knowledge of any of them in cattle or pigs, and none in sheep.
I didn't realise there were two different hormonal treatments, but from your post it would seem that sponges are akin to the pill, deferring ovulation until removed, whereas PMSG brings ovulation on? or just forward?
A friend worked on a farm that uses invasive AI. He seemed to be of the view that the type of AI I am used to in pigs and cattle doesn't work in sheep, so there is a technique that injects the semen directly into the fallopian tube, through a small incision made in the body wall.
We also know that flushing and embryo transfer / surrogacy is now happening in commercial sheep too, and sheep such as the Valais Blacknose.