Why wouldn't you take N Vancouver? You ride right by it on Broadway as you go down to the bridge. Just take Killingsworth or one of the other less heavily traveled east/west streets to N Vancouver and take that down to Broadway and over the bridge. Vancouver/Williams is one of the nicest streets for bike commuting.
If you don't want to take N Vancouver, you could try taking NE 7th instead of NE 15th down to Broadway. I haven't ridden that street during commute times, but other times of the day it has less traffic than NE 15th. But it doesn't have striped bike lanes, so you still are dealing with being a part of the car traffic.
I think most people here will recommend that you go over the N Vancouver if you are concerned with riding in traffic on NE 15th. On the Vancouver/Williams couplet, you get some nice wide bike lanes (some of the widest in Portland) and there is lots of bike traffic to keep you company.