The research continues. I haven't done a research project like this since I left school and I'm enjoying it!
By cross referencing the "Tree Book - Learning to Recognize Trees of British Columbia" and "A Field Guide to Trees of the Pacific Northwest", I have determined that there are 24 trees native to our area. (The Field Guide is also available through KNOWBC.com, the online British Columbia Encyclopedia.)
A tree specialist at the City of Vancouver has promised to help me out and I'm continuing visits to Queen Elizabeth Park. Not bad progress for a week!