Euh ... It was absolutely impossible to close it with the padding! I may retry lol but I'm surprised that you was able to close the player with it...
Edit:
I tried again but when a side is "clipped" the other side unclip... And I don't want to damage the battery

. Look...

There is my player with my new battery.

I'm unable of closing it because of these plastic part next of the black rubbers...

When I try to put some pressure the aluminium that are around the battery is deforming ...

(Look at this picture and also the second one, we see it better.)