I worked out a theory on Burori about a year ago, to explain his slightly different transformations. Lemme see how well I remember it. There are at least two major arguments for Burori being the LSSJ:
Aura: He has the odd, slightly green aura, never seen in another SSJ. There are only two other characters with this same greenish aura, Lord Slug and Bojack. (Movie characters, yes, but permissable since Burori is as well.) Bojack was a demon, therefore totally evil; Slug is stated to be an 'altered' Nameksei-Jin, therefore almost anything goes with him. My theory is that this evil 'soul', if you will, affects the way their auras appear.
Power level: He was born with a power of 10,000, an insanely high number for even a Saiya-Jin child. Simply put, no-one is that strong at birth except him. However, flashback to the manga, on Namek. Ginyu comments about Goku being a mutation, like himself, someone born with a particular aptitude for fighting. The word 'mutation' denotes something physically different, which makes it possible that Burori is a mutation in the extreme, and it affected his power level.
Bottom line, I just don't believe he was the LSSJ. He was powerful, yes, and he has chacteristics that don't fit in with normal SSJ, but there are betetr ways to explain it than him being the LSSJ.
I had other notes, but I can't remember them now, sadly. I also put it much more convincingly than this lol.
