Hi,
Here’s a link to a [https://www.youtube.com/watch?v=y3CCJtD0jYc|video] that shows how to completely dis-assemble the camera.
At 6:29 minutes into the video the section containing the battery cover is seen being removed from the camera.
I do not know if you have to dis-assemble it that far but hopefully the video may help you to at least gain access to the lid.
Have you noticed the [https://www.ebay.com/itm/Repair-Parts-For-Sony-A6000-ILCE-6000-Battery-Cover-Battery-Door-Lid-New-Black/152829472569?_trkparms=aid%3D222007%26algo%3DSIM.MBE%26ao%3D1%26asc%3D20160323102634%26meid%3D33d0cfeaf1d64e628716d82429852247%26pid%3D100623%26rk%3D1%26rkt%3D6%26sd%3D371837134380%26itm%3D152829472569&_trksid=p2047675.c100623.m-1|cost] of a replacement part? There are other suppliers but they are all around the same price. It’s even more if you have [https://www.ebay.com.au/itm/Sony-Alpha-a6000-Mirrorless-Battery-Door-Cover-Lid-Repair-Part-DH7178-/371837134380|this model A6000] It seems a lot to pay for a small (is it plastic?) part