The garden has a website with contact and other info. You could probably contact them directly to ask about early hours for photographers. (I have photographed there, but it was quite a while ago. Hopefully locals will have more info.)
Nature Photographers of the Pacific Northwest (NPPNW) will be holding their Fall conference in Vancouver, WA on Sat., Nov 8. They have a fieldtrip to the Portland Japanese Garden on Friday, Nov. 7 with early admission. Limited group size for the fieldtrip. You might want to check it out.