I did it last year on my 2012 rMBpro after it have been complaining about servicing the battery for about a year, and while it wasn't a walk in the park, it all worked out great.
Tip: there are 2 ways to replace the battery.
One is by following the official iFixit etc instructions where you remove absolutely everything before you peel off the battery with acetone.
The other is by immediately peeling off the battery right away. In that case, you have to be careful that the acetone doesn't flow onto the speakers (because they'd melt.) That's the way I, and many other with me, did it. It still only took me about 1 hour to get everything back up and running.
They did say that they might need to replace the shell (battery was slightly swollen in both machines) and that I'd be responsible for that cost, but that didn't happen for either box. I don't think they replace the shell unless it's really, really deformed. Neither of my machines would sit flat and both were obviously swollen. One I could practically spin like a top (and the trackpad was screwed).
I got both back with no deformities, a new battery, keyboard, and trackpad, and a 199 bill (plus tax).
I wouldn't rule out getting it fixed. If you do end up paying a little more, then you can probably sell it for more than the price it cost to fix.
Last time I looked I was quoted somewhere in the neighbourhood of $600 for a rMBP battery replacement - but that was just the battery. Even that IMO is not a reasonable cost for what it is - the only reason it costs that much is the fact that it's glued in, and the fact that Apple charge so much for the part.
Replacing a Macbook battery should be a routine task for any of them.
You can also replace the thermal paste, although now that it's not overheating all the time, I won't have that done until next time it overheats and slows down and I need to have it vacuumed out again.
i bought an $80 battery (ifixit? i can't remember now) and took it to a local shop and had it back in 3 hours. they charged $120. So... ~$200 but I had same day replacement.
* Advice from the internet: procede with caution.