The title of this is fitting and quite clever. The story's decent, too. I just got tripped up on two small things and one big thing, though.
1 - "egg-shaped black plastic". I really question the need here to describe the walkie-talkie; it's an awkward description, sort of alien-like. If you just say "walkie-talkie" or "hand radio" or something here, that would be just as effective and skips out the awkwardness. Most of us have seen a walkie-talkie and will fill in the image with the walkie-talkie we're most familiar with. I don't think the plot hinges on knowing exactly what kind of hand radio they're using.
2 - "Jesse loved it when she called him by any name other than what was on his birth certificate." Way too amateurish-sounding for you. Would he really sit in his car and think, "Yeah, sexy, not like the name on my birth certificate" or would he sit there and think, "I love it when she calls me pet names" or something to that effect. We're not stupid. We know things like "Sugar" and "Sweetheart" aren't going to be on his birth certificate, so there's no need to specifically invoke it. Likewise, "She sighed over the 20-mile lifeline." The important thing is that there's distance between them, not that there's exactly 20 miles between them. "She sighed into radio lifeline." or something to that effect would have sufficed, since we know there's distance between them from the fact that they're not right there together.
The bottom of this story falls out when you ask us to believe he doesn't know she's married. It's not consistent with the character you presented, and consistency is so important in writing characters. I don't have a problem with the readers being surprised that she's married -- I think you handled that quite effectively and that reveal should be saved for us, just as it is -- at the end.
In fact, I'd say very little here has to change at all.
You told me to stop reading what's not there, but I was reading what is here. Look, you even have these lines in here: He noticed when she got her hair cut. He knew how she took her coffee. He told her 'good night' when she left for the day. and He didn't even care about her a two-pack-a-day habit. He would know all these things but not that she's married? Wouldn't he see she's got a wedding band on, at the very very least? Again, it's his business to know things and find things out. Knowing all this about him from all the other details right in your story, you think he's really not going to know she's married? You want your readers to be imperceptive? Really?
To fix this problem in your story, all you'd have to do is tweak the spin. It doesn't even require heavy editing (which I know you're not fond of anyway). Instead of being in shock at the end, he can just get really, really pissed at being reminded. You wouldn't even have to change his reaction -- just take out the indications of his surprise. Everything else still works, and even would reinforce it: he reads like the kind of person who always gets his way, always gets his prey -- demonstrated by the way he brow-beats and intimidates his informant (right in your story). But Veronica's the one thing he can't get. He wants to keep trying, can't bring himself to leave the business, but he just can't get her no matter what he does. We don't know why he can't; he doesn't really seem shy (no problem getting in real close to Judy and harassing her, no problem flirting over the walkie talkies -- once again, right in your story), so why can't he get her? At the end we find out she's married -- Oh. It would just make more sense if he knew all along, which is reinforced by the bit about his daily anguish (right in your story).
That's it. Real tiny and real easy fix, not even painful.