I do think later July rather than May (or early June) is likely a factor. This year at the box office, though, has been an unusual one. "Franchise fatigue" (generally, not Trek per se) is probably also a factor. Moreover, movies are expensive. I can afford it, but a family night at the movies (not seeking "half-price Tuesday" or matinee prices)--four tickets, two popcorn and four drinks (not necessary, but typical) easily pushes 85$ (or over 100$ if IMAX 3D). As a student years ago, I routinely saw 3-4 movies a week (no TV in my apartment for 2 years). Even accounting for inflation (of my available money then), there's no way I could have done that today.
The issue of marketing is tricky. I think it was crammed too late to be fully effective, but there are a few factors to consider. One--very tight production schedule (not quite as catastrophic as the pressure for TMP, but probably the second most problematic of all Trek films). Two--cost of massive, lengthy marketing campaigns. Paramount is not facing MGM style financial problems but it's also not Disney or Universal, or Warner Bros. for that matter. The late production makes less material available for marketing and, if the studio is bleeding money elsewhere (as appears to be the case), perhaps it adopted a "penny-wise, pound-foolish" mindset to the marketing campaign.
The one thing I feel pretty confident about is the irrelevance of "fan" (as opposed to general audience) attitude towards the reboot Trek. The number of fans who truly refused to see the film(s) pales into insignificance vs the general audience. Also, the latter doesn't care--at all--about what hardcore fans think of the movies. The studio is pursuing the general audience, not the fans (fair or not, they simply--correctly in the aggregate--presume the fans will see it anyway, likely more than once). So Paramount will be trying to figure out why the general public didn't turn out as much as for the previous two, not worrying about "the fans".
I also think home video (in all formats--disc and streaming/downloads) will matter more than for previous releases (this is a general trend anyway). I recently read an article (can't remember the movie) that talked about a movie from six or so months ago that was rather a flop (Beyond is already a bigger moneymaker relative to cost than the film in question) at the box office but home media sales/rentals/streaming have made it a rather profitable project overall and may well earn it a sequel. So, unless Beyond actually loses money at the box office (highly doubtful), I think home media will boost it enough to warrant at least one more kick at the can. After that, I doubt the cast will stick around, so there'll be some other Trek at the cinema later on.