wrote you nice answer to this, best i could, and laptop battery died right before i hit submit. hate when that happens. got to get ready for church, but...
the progesterone to kickstart af is usually provera. i believe they give it most often as like 5 pills. i think some use a shot, instead. if everything else is normal, when you stop the provera, you get the withdrawal bleeding, like you said. if you dont bleed, they have to look for another answer, like maybe you need an estrogen/provera regime, and they need to figure out what's the cause. if you just had a fluke anovulatory cycle for no good reason, taking provera and starting your af should help end that long cycle, and then hopefully everything will go back to normal (if there isnt something else funky going on to cause the problem.)
there are tons of different progesterones out there. pretty much all the bc pills have different ones, so if you've ever taken one bcp and it doesnt agree with you, like you gain wt, break out, whatever, you can switch to find one you like.
the one we take for luteal phase problems i think is pretty much straight up naturalish female progesterone. the brand name is prometrium (or is it prometria, i forget.) it takes over for the corpus luteum, so that if the c.l. concks out, our bodies dont catch on, and we dont get the signal too early that 'there wasnt a pregnancy this month, so bring on af' until we know for sure that there really wasnt a preg, and then we stop it, and af comes in a few days as prog is cleared out. i think this is the one they use for pregnancy because it is considered safest in pregnancy, most natural, but i think some docs use this same one to bring on af too.
if we get pg, we keep taking it till placenta takes over for c.l., like 12 wks, although, when i was pg with ds #3, i wasnt on prog, and my corpus luteum cyst burst at 9 weeks. i sat up in bed one morning and had this sudden excrutiating pain, saw stars, and about 30 mins later started bleeding in the shower with a walnut sized clot plopping out. i was hysterical. my ex-dh, who is an obstetrician, took me to his partner- he went into dad mode, not dr mode, cuz he freaked a little too, and anyway, i got an ultrasound and i had blood in my abdomen and a broken cyst. they did not put me on progesterone at that time though, talked about it, but decided placenta was ok to take over, and it did, and i had no further problem.