Downtown to SWCC
I used to live in this area and here's how I'd do it (if I was pulling a trailer):
Broadway -> Terwilliger -> Barbur (right turn) -> Bertha Blvd (right turn) -> Vermont (left turn, ready to climb a hill now?) -> Capitol Hwy (left turn) -> Vermont (again, where Capitol Hwy veers to the left, stay straight). Now you just stay on Vermont to the bottom of the hill, past Gabriel Park to the SWCC. This is a bit longer than the previous route recommended, but it avoids the stress of Capitol Hwy from Terwilliger through Hillsdale. The worst part is a short stretch of Vermont past 30th Avenue to around 34th, where there is little to no shoulder, but I've found traffic to be cooperative here.
Returning it's a long uphill haul back up Vermont, but just reverse the route. If you prefer you can return via Barbur Blvd (and bypass the challenging left turn onto Terwilliger from Barbur) to downtown (to Naito or 4th Ave).