The “flip up” tab was hard to see for me but once my 7yo confirmed it was up, I slowly moved the cable into the slot using my fingers (to avoid bending/breaking anything, thanks to comments I read), staying perpendicular. Once it was clearly in, I confirmed it was fully seated with a toothpick (a gentle tool for delicate parts). If worried, take zoomed in pictures straight from above, that way you will know what it should look like when reassembling.
This was a piece of cake, thanks to all the comments, and to my 7yo who taped and color-coded of all the screws on a sheet! I used very little heat probably because the batteries were very swollen. I used the acetone (sold with the kit) only to remove the glue.
At the last step reassembly there was a 1-2 mm gap between the cover and the body. Upon inspection I found that one of the new battery’s plastic bar had to be gently nudged under the aluminum « post ». At the ends of the plastic U shape, look for tiny flat protrusions, right next to the rubber bumpers, those should go under a recess near the screw posts (one can be seen on the left of the thumb on the image above).
After I put the battery back I found out at this step that the new battery connector was off by 2 mm (because I installed my battery slightly off). Since the connector is rigid, I removed it’s plastic cover (just like we all did in Step 4) to free the cable, which allowed me to bent it enough to properly plug the connector.