I prefer the hyphen, Elewina, which isn't to say sans hyphen is unacceptable. Apparently, given your sources, we've a choice. As you may known, hyphens have a life of their own. Initially, a hyphen is introduced to add cohension, and once settled in its orthographic place, writers begin to omit it for sake of efficiency. It's viewed as no longer necessary (the assumption being, the units it ties together have evolved into a single cohesive unit) which is a process of language change that's seen elsewhere in the grammar; i.e., omitted phrases and words; e.g., the conjunction "that". The hyphen is like a conjunction, right? How many writers and speakers still add in the conjunctive "that"? It has it's purpose in some sentences, but not all. It's fading away. Language change like that, even something as small as a puntuation mark, takes time. While some writers maintain, say, the hyphen, others will omit it, in the same way that some use "that" and some omit it. In the end, as long as writers are consistent in their use, there shouldn't be a problem. The hyphen has one purpose only: to ease the reader's burden. And that in itself should be our only guide. Personally, I find "level-headedness" more reader friendly.
All the best.