I decided to make this ticket depend on #11943, for two reasons: Firstly, it is rather clear that #11943 is a good idea, while I am less sure here (it is good for speed, but may under very particular circumstances break new pickles). Secondly, #11943 seems less invasive than the patch here.
I think that the "potentially breaking new pickles in a distant future" aspect is less urgent with the "weak pickling by construction" approach. Hence, I have only updated the second patch, the first can now be disregarded.
Apply trac11935_weak_pickling_by_construction_rel11943.patch