Like many here I also did not remove any components, but used dental floss to cut through the sticky pads holding the battery to the top case, and did not apply any adhesive remover. Using a sawing motion and firm (but not too firm) pressure you cut through the glue fairly easily. It was more work to clean up the residue left behind - for that the adhesive remover was useful! I was quoted between €300 and €500 by the local apple authorised service centre, the €90 iFixit kit is great value. Also much more fun to do it yourself!

Thanks great instructions. On the Yanec replacement battery I bought, I had to manipulate and bend the cable holding the connector to the battery quite a bit to get it to stay connected to the motherboard. Once I did that though, all good.