I have run into a similar situation but on a thin, busy road. One stretch of my commute, about 200ft long is perennially packed with parked cars. The road is technically a 45, but 60 is probably more accurate. My choice is to either keep to right, and hug the cars, perhaps weaving in small gaps and giving traffic room to pass. Or, take the lane for about 200 ft.
Once you can make the initial leap of faith to take the lane, its smooth sailing. Alternatively sometimes I just don't have the emotional energy to take the lane and try to squeeze to the side. Usually when I do that I am in panic the entire time, and ride very nervously.
If I was a better cyclist, I would choose option 1 every time.