Until I went onto Progarchives, I am fairly certain I had not heard of the term before. I get from reading the description that for prog (on this site) it means to 'crossover' into popular music influences, though it also includes bands that 'crossover' into alternative rock or other commercial brands of music. For whatever reason, the term bothers me. Maybe it's because I usually think of the word crossover in terms of basketball, not prog.  

You are correct. 

 

And for labels, I think the important thing is to focus on what the label means as oppose to what the label is. (Which you've got the right idea of it btw)

So, you're puzzled with that "crossover prog" label? Only that one? Nothing to say about "eclectic prog", "prog related", "heavy prog" or "proto-prog" (okay, this one may be recognized as a "legitimate" label, but it's not like it is a genre per se).

That "crossover prog" thing, just like explained by Man With That, results from the splitting of the Art Rock category in the PA database, and that's all about it: it's not a term used by anyone out of PA, because it's a convenient way of categorizing groups and artists for PA, even if one can doubt of its reliability from a musicological point of view (on the other hand, RIO is used as a musical category by some and... well, listen to the RIO musicians for yourself and take your conclusions!)

^ No, on this site it's a carefully considered term for prog rock that crosses into pop.

I also hadn't heard of the term before I joined the site, but must confess that this sub genre makes a lot of sense to me. I was in the Crossover team for quite a while, and as Atavachron says, it is a carefully considered term - have a look at the genre page to understand more. It isn't a dumping ground for bands that don't fit in other sub genres, but is a valid entity in its own right 

Given the origins, I am curious if anyone knows some of the labels that were rejected along the way before settling on crossover. For example, was "pop prog" or "alt prog" or "hummable prog" considered? Is there thread for rejected prog categories?

Many of the bands listed here under prog related, crossover, and even heavy prog could all easily fit under the same roof.

Well that would be one for me. It was my baby though not without the help of rest of the baddest bunch of musicologists, rustlers, cut throats, murderers, bounty hunters, desperados, mugs, pugs, thugs, nitwits, halfwits, dimwits, vipers, snipers, con men, Indian agents, Mexican bandits, muggers, buggerers, bushwhackers, hornswogglers, horse thieves, bull dykes, train robbers, bank robbers, ass-kickers, sh*t-kickers and Methodists that this site ever saw.  We were the ones that evaluated the sh*t show that was the old Art Rock grouping that had been a dumping ground of musically dissimilar groups.  We evaluated every single one of them,  think it was around 800 IICC David?

Which I'm glad for, because everyone else has their own definition because it's such a general term.

It's not phrased perfectly, but I think that it's saying that classical, jazz, and folk are more inherent or traditional prog influences, and that crossover prog bands often can have a significant influence from mainstream music in addition to those genres.