Sounds like you would like to more formally add one of Karl Popper's criteria for what constitutes a true scientific theory (perhaps we could add at least a testable philosophical assertion as well?).  In short, I like with your proposal and it might give better direction and interests to the forum, the journal, etc. I would think that one of the first steps is to identify an outline of important assertions made by big historians that are either key to the discipline, or those that at least are somewhat unique to it. For example, the field of paleo-anthropology is continuing to revise many of its beliefs as ancient fossils and artifacts push various time and space boundaries of early human history ever further it seems (some key "facts" in the tale told by big history). How and why complexity has increased over billions of years, at least in our little corner of the cosmos, or key changes wrought by agriculture in social energy flows, would be a couple of relatively unique interests of big history.  Someone with a well-established authority and broad understanding of big history like David Christian, Fred Spier, Andrey Korotayev, etc. might propose just such a outline?

I agree that an assertion, or at least implication, that goes something like: "life's spectrum of increasing complexity is but a continuation of increasing abiotic complexity," likely has a lot of room for discussion. (An assertion of  increasing abiotic complexity seems harder to refute on both an empirical and physics level).  Coincidentally, I am rereading David Layzer's  book, Cosmogenesis, and I happen to be at the section of the book where he somewhat addresses your proposed query as well. For example, he points out that complex organisms, like mammals, also seem to have an increased ability for making relatively rapid macro changes compared to simpler organisms, like bacteria. Hence, entertaining the notion that life's increasing complexity is but an epiphenomena of what is actually an underlying increase in the potential for life to rapidly adapt is an intriguing one. (Look at how rapidly mammalian species radiated after the KT catastrophe compared to bacteria, or even crocodilians for example.) I've not read “Major Transitions in Evolution, Revisited”, so I can't comment on its insights, of course. 

Back to principle point of your suggestion,  rigorously questioning and testing the core premises of a discipline has historically often been a fruitful enterprise with surprising discoveries - a point I won't belabor because most big historians are already aware of this.  Adding some order and priorities to falsifiable big history tenets (and even some proposals on how to do so) would be a grand and relevant project.