Excellent idea, I think I'll do just that....
FWIW, it seems you *can*, at least under some circumstances, start a "missed" story arc by phone.
At level 38, my contacts are running short on missions, with mostly timed missions or "arrest 40 guys" missions, or against annoying enemies like the DE. So I started calling my contacts to see what they had, found an older one with a mission... against the DE, but what the heck....
And discovered that was the start of a lvl 35ish story arc I'd missed because I tend to avoid the DE, since they're so annoying to fight. I actually did get *some* experience, but everything's green or grey....