Solidus, you layed the facts out but didn't give an answer, so no we cannot lay it to rest. Besides, if you actually watch a legit copy of movie 4, his hair doesn't go red, it goes black with gold highlights. The form where the muscles and ONLY the muscles swell and the pupils dissapear is USSJ/Ultra Trunks (sub/dub), which Broly does not transform to.
Gir, you're making no sense. We're not disputing that he is the Legendary Super Saiyan, we know that, it says it on the box and multiple times throughout the movies. You can't say he simply IS the LSSJ transformation, as he has three other forms, so therefore we must assume that it is a different form from SSJ, and all the signs are there that it is. This we understand to be a form unique to the Legendary Super Saiyans born once every thousand years. This form (or stage if you prefer) we call Legendary.
Therefore his states are Normal-Giji-Super Saiyan-Legendary. Maybe we should call the Legendary form something else so as not to get confused, for the sake of simplicity i'll refer to it as SSJX.
To summarise:
Broly IS the Legendary Super Saiyan.
His transformations go Normal-Giji-Super Saiyan-SSJX.
Whereby SSJX is the form understood to be Legendary.
EDIT: Forgotten: That's correct. I don't know if his hair is blue, but its the second pic in post #7, dark with gold highlights.