I have been playing the culture flipping method a lot in the past two weeks and I totally feel the shipyard should be flipped along with the primary planet sponsor. It makes the most sense as it really is an extension of the planet.
Perhaps upon culture flipping the shipyard could be inactive for several turns until it is fully operational under the new owner.
But yes, I hate the Shipyards just sitting there in my territory - and I can't attack them without declaring war. At the VERY lease the AI should migrate them within their own borders. But that seems overly complicated so changing ownership still seems more logical.