See with us we hatch the majority of ours with a incubator & from a trio of birds doing it this way I normally get 50-70 eggs a season with them & normally in a good year get around 95-98% hatch rate, By doing this it leaves me with approx 20-30 xmas birds & a few to sell on, A lot I sell as goslings or sell some eggs, sometimes with geese I do find if your having a bad year hatching some then normally everyone else seems to, it's the same thing with "July sprawlers".
I am do let my females sit late in the season, my young birds did sit last year, but got impatient towards the end & didn't hatch anything but they did rear goslings, so I'm going to try again this year, I have in the past let geese sit but my last 2 females that died last year, never hatched anything despite being very fertile, they would sit every year but just crush eggs or goslings when hatching or rats would steal eggs from the nest, so we just hatched all the eggs in our incubator & let the geese rear them, from about 2-4 weeks of age - mainly due to our geese free ranging & predators such as rats in the shed, foxes & red kites / buzzards & us having a river, which they did fine, Ironically the gander used to take to them 1st. We always introduce them using a run as our adults can be very over enthusiastic to get to them & goslings to have a tendency to stress out & die, so we do this gradually as geese can be aggressive so it helps if to stop them attacking them - you won't know unless you try, ours have been very good at accepting young.
If your worried about birds being related, you can sell or swap the male or always buy eggs in, then you have a new bloodline & swap the gander then - we've eaten birds that are 3-4 & they tasted fine, Hatching in incubators you just need with ducks & geese to have the humidity around 40% & upto 50% for hatching temp around 37.5 C & make sure the eggs are turned twice a day, & candle eggs every few days or once a week in a dark place to check for bad eggs as a rotten one can spoil a whole batch or if you haven't got a candler I find in the last week with any eggs get a bowl of water & put the eggs in for 5-10 mins & the ones that move once the water has settled have something in as you will normally see them move quite a bit - not always but if your uncertain keep those eggs, I also never rear geese on heat, But I normally keep them in a warm shed fed on water / bread & milk for the 1st 1-7 days & have them on grass in the day, with a tray of water just not too deep, maybe a inch, & they thrive.