Around here, shops won't touch parts a customer purchased let alone install them. Two reasons why are liability and profit. First, if they install parts you bought off of Ebay, or some bargain-basement.com site and something happens, where's the first place you'll be going when the part fails or damages something else? The shops would rather get the parts from known distributors that they have some sort of guarantee with. Secondly, they stand to lose some bucks installing your parts. The parts they get from local suppliers usually get a nice mark-up added to the cost before it hits your final bill.
I'd imagine it's the same in B.C. or anywhere else in Canada.
Try shopping around. You may find a garage that's cheaper than the one you quoted earlier. Just because it's $670.00 at one place doesn't necessarily mean it's the going rate all over town.
Better yet, just drive across the border into WA. $670.00 canadian is like $20 US right?

That's a steal of a deal

j/k