Late Spring/early Summer is definitely a bad time to have your plane
laid up. Ideally, an Annual should be only a few days. However, if
something has to be pulled and sent off for repair it can stretch into
months. Years ago now, but an AD required that my prop blades be shot
peened for stress relief. Only two places in the world did that - one
in Canada, and the other in Germany. It took awhile...
Depending on the weather where you live, late fall is a good choice.
My last was in November/December. Fortunately, the weather cooperated.

David Johnson