Replacing battery in mid 2012 15" MBP myself - using genuine Apple battery?

I've got a mid 2012 15" unibody MBP, non retina (one of the last easily user serviceable ones).

I have used it every day since I bought it in early 13 and the battery is pretty weak now, a full charge lasts about 1.5hrs. (the 2:29 remaining shown in the screenshot seems inaccurate when you actually use the laptop)

If I click on the battery tab I get this service icon. Ideally I don't want to have to book an appointment, go to the apple store, lose use of my laptop for a day etc.

Can I purchase an official Apple battery directly from Apple and do the change my self? (I know there are lots of 3rd party batteries on Amazon / eBay, but I want a genuine part.)

According to several sites, which mostly point back to this iFixit page, "...Apple informs its own service personnel that 'batteries must be replaced with the top case assembly' and that 'the battery alone is not a replaceable part.'"

Also, iFixit found the following when trying to remove the battery:

• Someone really did not want the battery in the MacBook Pro to come out of the upper case.
• We tried valiantly with our iFixit 6 Inch Metal Ruler to free the battery from its aluminum confines, but to no avail. Rather than risk puncturing a lithium-polymer battery cell, we left the power source in place.
• To complicate matters further, the TrackPad cable lies underneath the battery. Attempting to pry the battery off the upper case could easily sever the fragile cable, which would be bad.

It might be best to just take it to Apple to get the battery replaced. It appears to cost US $200 for a new battery.