I've thought of a couple of examples from other shows that illustrate more the direction I hope they'll go. In a later season of M*A*S*H, there was an episode where Hawkeye and Margaret were trapped in a farmhouse during intense shelling nearby. There was a real chance they might die, and they were terrified. In that instant, they turned to each other for comfort, including a passionate kiss. They were eventually rescued, never speaking about what had happened. They'd known and respected each other for years, despite some early hostility. There had been some sparks of interest, and they gave into those feelings briefly. But they knew a long-term romance was not in the cards for them, so they moved on but treasured that experience together.
In the ST:TNG episode I mentioned earlier ("Attached"), Picard & Crusher were connected mentally and shared some of each others' thoughts. They admitted there had been some attraction for the other (especially Picard for Crusher), and added to their shared experiences together, there was a romantic spark struck. But they eventually realized that the deep friendship they shared was more important to them than the possibility of a romantic relationship that could easily end and destroy their friendship. And so they continued, enriched by the experience, and still connected as friends. Heck, even in the possible future of "All Good Things...", they'd tried marriage and it had failed. And while it apparently didn't completely sour their friendship, there was more strain and distance.
THAT is what I'd prefer for Coulson and May. Acknowledge the attraction and spark between them, but realize that their friendship is more important. You don't need to be in a romantic relationship to confide in and support the other. In this age of cheap TV romance, that would be the harder choice for the writers.