Ed...I am not suprised that the igloo eventually collapsed. In the Central North Island of NZ we are kind of poised between a cold Antarctic air mass to the south and a warm tropical one to the north. In the winter the southerlies usually dominate but it can happen that we will get a tropical depression come down from the north into the Bay of Plenty. This can bring lots of rain at any altitude. It isn't unusual for the skifield's to get good snow and then have it washed away in a couple of days. What is left can turn out as either slush or ice. We are planning to get out and have another igloo trip soon, hopefully I will get there this time. Need to start earlier and have more shovellers I think. There is no way I want to freeze my toes off in a tent up there.
It's understandable then that the igloo could collapse and the rain certainly has a big influence.
An early start on building the igloo is wise but more shovelers just makes more work if they all intend to sleep in the igloo. Pretty much just like a snowcave where each person is tired by the time the cave is done.
Also, inexperienced people need to learn and the more that get taught, the slower the igloo goes up.
One labor saving choice is to sleep three in an eight foot igloo but this requires not having a trench down the middle of the igloo to hang your feet into. Being able to sit and relax with ones feet hanging is a large part of the benefits of igloo living.
I hope you have deep snow for your trip.
We made another flash-looking igloo on Ruapehu near the Ski Lodges. Hard shovelling but easier packing. Had a good night's sleep. If the forecasted bad weather arrives it should last if the rain didn't melt it 1st.