The family register is definitely a problem and it seems Aki really want's one, adopting is also hard I think since they're not really registered as a couple and you need to process legal documents for that.
Though as for the gene thing it should be fine, if I recall the chances of defects for 1st gen is actually non existent (around 1-2% more chance of regressive genes being passed to the child than your normal couple), it only becomes a problem with 3rd gen inbreeding.