Thanks for your comment! It was really essential since dropping the battery in the case without its control card being attached could have resulted in the impossibility to connect it.
I don't see how starting from the side is even possible, it's too steep and the card is not flexible enough.
I started from the top. To do so, I had to lift the battery control card (step 24) enough to be able to put the power connector (step 15) back below it. That way I could slide the card all the way.
Because of the way the tutorial describe it, I was conservative on the quantity of remover. That may be why this step was not easy.
Agreed, hardest step. “Several drop” was not enough, I had to add more twice, so take your time.
Just like on the picture, the corner close to the track pad seem to be a weak point, strat pushing the corner of the plastic card there.
The air drier worked well for me, just need to be patient and and maintain a slight pull force to know when it's ready.
I did not need to secure the cable, the glue on it was still effective, apparently.