Just came back from a solo on Gannett last week and I'm not quite sure why you experienced such difficulties. There are a couple ways to access the Gooseneck Glacier, including the way you started, by traveling up the Dinwoody and then climbing over the rock between the two glaciers. One could also climb straight up the rock and rubble at the base of the Gooseneck.
You wouldn't have seen the bergshcrund becuase its on the Gooseneck Glacier, you were entirely in the wrong place.
Also, the glaciers seem to have receded a bit, which makes the use of the Dinwoody Glacier unnecesary.
It isn't a bad climb, definitely easier and safer for a solo climber than Granite (in my opinion.) The crux was definitely the slope just above the bergschrund. It is steep and the ice is very hard. It seemed to me like a no-brainer to opt for the rock which was actually very easy. The only difficulty here was moving from the glacier to the rock. That move is on a steep slope and is awkward. I thought it best to dig out some steps with the axe.
I think a rope would be necessary on the steep snow slope, but not on the rock, provided you are comfortable on such terrain.
My thanks to the Wingpeople for their recommendation of the Cowboy Cafe. Perfectly good food and pleasant people to boot.