That's a good question. I like the Melrose idea. I have an irrational fear of biking westward over that Lakeview overpass. I say it's irrational because visibility is pretty good for motorists and the road is pretty wide, but sometimes people go pretty fast there.
It also dumps you off on Eastlake, which isn't ideal, but you could take your next right and squirrel down through SLU on Republican or Harrison. They both go all the way to Dexter, but they also force you to cross a couple of busy streets with no lights (Fairview and Westlake off the top of my head).
So I guess the question for me would come down to: is my perceived risk of the overpass and crossing Fairview and Westlake at uncontrolled intersections greater than my perceived risk of biking down Denny? That's something that only you can answer for you, of course. I'd have to try it before deciding, but I'm more comfortable riding with the flow of heavy traffic than I am with crossing against the flow of heavy traffic, so I think I'd lean toward Denny. I've done Denny a lot, though, so there's definitely some familiarity-bred contempt there. I'll try out your Melrose->Lakeview->Republican->Dexter idea next time I'm biking from Cap Hill to Fremont.
Another question: what's the best way to get back? This seems like a route that might have a better alternative than simple reversal. I might be more inclined to take stinkbug's Burke-Gilman route on the way back, in part because the hill climbs seem more gradual. I hate climbing the Denny overpass. My chain came off halfway up once, and I fell against the high curb. No fun.