Using a friend as an AI sperm donor, what things will increase our chances of conception?
Timing is obviously essential, since it will hardly be an option to attempt AI every other day. What method are you using to pinpoint ovulation? I would say ovulation tests are a bare minimum. Only counting days could have you inseminating at the wrong time every month. Ovulation tests detect the hormone surge that (usually) triggers ovulation. To be sure ovulation actually has happened, you can chart basal body temperature. Which means every day first thing starting at the beginning of your cycle. Research Natural Family Planning or Fertility Awareness. Then there is sperm delivery. Obviously as fresh as possible. If he brings it over, it should be within an hour of ejaculation, and kept at the right temperature. The inside pocket of his coat should usually work. A bag would be too cold, next to his skin would be too warm.
You need to speak to a lawyer about this, because he will have every right to come along and claim the baby as his child. Conversely, you could go back and force him to establish his paternity and file for child support. Go see a lawyer and get this hashed out. You won't be able to file for paternity and then do the termination of parental rights/adoption until a child is born, so this is a huge leap of faith on both sides. If you do nothing, you're leaving yourselves open to a lot of trouble down the road. Go get a lawyer involved, so you minimize the risk.
There has been great success with traveling to Hawaii and doing AI in the ocean with the assistance of wild dolphins.
Going to a reproductive endocrinologist...
Go through a reputable fertility doctor.