Sanesh, I think your best bet would be Central Valley Greenway from Science World (or St. Augustines) all the way to Lougheed Mall. Separated bike path down Lougheed Highway to Colony Farms. Then take the Poco Trail all the way up to David Ave. East on David, then up Oxford. Top of Oxford is a trail, take that then across the river out to Pioneer Park. Up Marguerite Street to the trail on the right up to Coast Meridian. Then up to Harper.
It might be a longer distance, but that whole route has minimal stops, lots of gravel, separated routes, and might be faster with less stop and go. It also has minimal elevation gain until you get to Burke.