I like the 1st two but the 3rd kind of limits creativity. For example someone might want to have a demogods that live in a tower and come down at night sometimes to create offspring. It wouldn't work if the males had to stay there for 9 months. Also makes it so that isolated communities would probably waste a lot of demigods before they realise how it works.
However you could have it work this way in your region since Lumuoles (especially great ones) aren't bound by many rules. Demigods that experience huge physiological changes probably would either work like this, take the power needed for these changes at the end of mating(trying to be classy here), or have to go through these changes some other time in their lifes with a lot more Lumuoles.