MP,
Trust me, I know how you feel. I made my first attempt at goose eggs last year... I only got one to hatch, she is my avatar... Lone geese are weird creatures, she is obsessed with my husband and sleeps with guineas (only thing as loud as she is, lol)
Thanks to a wonderful trade partner, I had some pilgrim geese eggs arrive at the beginning of March, the eggs were dirty like yours, I think especially with spring rains, they track lots of muck into the nests. Out of the five eggs that arrived from LA to AK, only one had a bad air cell. Out of the four left, by day 6, two were showing clear development. I have been fortunate, both of them were/are still developing and are now cooling on the counter so the goslings can turn in preparation for hatching hopefully on April 1... The excitement is definitely building as I heard cheeping coming from the pheasant eggs that I had set with them to check fertility, this has to be a good sign. I am keeping my fingers crossed for you as I get ready to set up a potential brooder.