I have always pre-shrunk batting except wool. It can be kind of a pain, as the batting can stretch when wet. Some brands specifically say not to pre-shrink, I guess because they don't want people to stretch it and then be displeased with the results.
Warm and Natural had directions on how to do it, which specified not to spin it wet; I laboriously squeezed the water out with towels, until some people on the QB said they spun it with no problem, so then I did, too. The hardest batting I worked with was Hobb's Tuscany silk, which was very stretchy when wet. Their wool-cotton blend is lovely and I took a chance on spinning it and it came out fine, and dried very nicely in the dryer
Having said all that, I don't know if pre-shrinking batting is worth the trouble. I measured a bat once before and after washing/drying, and it didn't shrink much over width but about 7 inches in length. Still, my quilts always crinkle much more than I would like even with the pre-shrinking, and even when I air dry them. I think your quilt looks beautiful, NZQ, and I would not hesitate to gift it.