I thought I would need 3-4 goes to get what I was looking for.
I decided to see if I could speed things up by boiling them in our pasta pot.
I boiled them for about 10 minutes. There was some advance on the felting - but also a lot of very dark dye leaching out, so I reverted to another round in the washing machine.
This time I added a tennis ball to the machine - hadn't tried this before.
The result was really pleasing. I'm not sure if it was the tennis ball, or the pre-boiling, but this time they were well felted.
They have felted so well I clearly didn't need two handles.
They have been warmly welcomed - and used - by the egg collectors!