I think half the problem is the stem direction. In the first example, it's easier to read due to the differentiation due to SATB (sort of), whereas the second example squashes it all together, with differences in the 'alto' part - notwithstanding differences in timings of certain notes.
The '4/4 v 12/8' question still stands, and there's absolutely no need ...
If you wrote it in 4/4 with frequent or constant triplets, you'd be in good company. That is how Beethoven rendered the first movement of his piano sonata number 14 ("Moonlight") and how Ravel notated "Bolero" (think of the snare rhythm).
The Beethoven sonata may be a very helpful model because the first bar or two is usually notated with ...
The 12/8 version is absolutely standard and would give no trouble to a reasonably experienced performer.
I agree that the 4/4 version is unnecessarily cluttered. It's not unusual, however, to leave out the triplet markings for groups of three eighths once the rhythm is clearly established. For example, here's an excerpt from the Mikuli edition of Chopin's ...
Something like this should be clear.
Responding to your comment:
OK, just one or two trem. bars then. Or this. (Whoops, I forgot to erase the time signature.)
BTW, have you tried playing it? Not at all comfortable, unless your hands are a lot bigger than mine!
I have seen (and use) them in my music to signify a legato or soft tongued phrase. Although this is only used by some composers/arrangers for big band/jazz orchestrations (a field where dots, dashes, accents and various other ornaments have different applications over the decades.) Gotta luv those crazy jazz guys! NO RULES!!