Okay, now I'm thinking (hoping) there is another possibility we haven't thought of.
At the end of the episode, we see the doctors & nurses rush in. But the episode ends before they call time of death. I've never heard of someone being able to make it after an embolism, ( my limited experience coming from watching medical dramas.

) What if he's simply hanging around (the whole show) in that near-death coma state?
You know, that place where people who have died & come back have said they hovered over their body and saw the crash team was working on them. Instead, Jim goes to Melinda, since he knows she can see him.
I remember something Jim said last season. They were talking about a "Do Not Resuscitate" order, and whether they would want to hang around in a coma, even if there was practically no chance of coming out of it. Jim said, if Melinda had already died before him, then to pull the plug on him. But if she was still alive, and there was even a slightest chance he could come back to be with her again, he'd stay forever.
We saw the previews where Melinda tells Jim to go on. But Jim wants to stay. Maybe it was just her saying he doesn't have to hang on in the vegetative coma, he should move on?
Maybe their "journey" is how their love for each other somehow makes a miracle happen, and Jim miraculously comes out of the coma, the doctors said he never would come out of, showing in the end, "Love conquers all."
Man, I hope it's something like that, instead.