My own inclination would've been to write Chekov's accent phonetically, "wery vell" and all that, but Marco Palmieri's preference was apparently not to render Chekov's accent in print, and so I learned not to do it. The main exception, which is unlikely ever to see print, was in
Seek a Newer World; since the 2009 film made a point of playing up Chekov's accent, I did include it there to fit the tone. I also tried to reflect the other Russianisms present in Yelchin-Chekov's speech, like occasionally omitting the definite article.
As for Scotty, I do include some bits of his accent like "dinna" or "I'm thinkin' o' doin' that" or that sort of thing, but I try not to do it to excess.
If this is true, should writers also capture Kirk's character on the page... by... INSERTING dramatic... pauses... whenever he speaks?
I've seen that done to an extent, and I've done it myself at times -- trying to match a realistic Shatner speech pattern rather than a caricature, though. In
Ex Machina, there was even a bit where I included that Shatnerism of pursing his lips and drawing out the "W" sound at the beginning of a sentence. I rendered it as, "W . . . we're working on sorting that out."
(I've never gotten why people mock Shatner's hesitations in speech. What he's doing is pretending his character is making up the words as he goes, thinking before he speaks, rather than just reciting memorized lines. I think it makes his speech more realistic. If you listen to real people speaking off the cuff, they tend to pause and stutter even more.)