What exactly are you trying to do? Just SFO-HKT via SIN? Are you stopping over in HKG? No, then don't put the city pair in. Return from SIN to LAX?
What travel agents are you booking with ? US or Canadian ones?
I don't know what this 'matrix' you are referring to.. but there are no W spaces for the 13th and the 31st. There are some "E" seats on the 14th. But other than that - nothing.
Trust your TA - they can see all the spaces there are available.