Having said that, my sensei certainly seems to know what he is doing, even if it is a bit odd to me. He trained with Nishio sensei, which is apparently why things are a bit unfamiliar to me.
I train some with a Nishio influenced sensei myself and at least in my experience, it's not that the Nishio style throws out the L shaped hanmi stance but that in certain situations one moves into an iaido-eseque parallel stance as a part of the tai-sabaki. One example being Yokomenuchi shihonage/ and or iriminage. Nage begins in hanmi but the rear foot moves into a parallel position(a la iaido kamae) before the front steps back while Nage cuts down/redirects the attack with his/her arms. But that is just from my experience. I also originally came from a dojo that used the foot turned out stance which you referred to as stance 2 in your first post;the dojo-cho was a former kenshusei of Chiba sensei. I totally agree with Joe in regards to this stance. When your hip is flexible it is very stable and quite safe for your knee but if you have tight hips it can put a lot of undue strain on the knee. This might be the reason that the dojo-cho from my first dojo does a lot of yogic hip opening exercises at the beginning and end of class.