Um... Well, I would recommend you do take out those screws... regardless they help or not... They are just an issue now if they are that stripped.
For my P2, It now does not have a back... What I did my help you. I use a cardboard peice for the cover.... But you can still use your back. You need art foam and maybe some duct tape. Take the art foam, cut it to size and place it over the batteries and then tape the back of the shell to the top like you did. If that doesn't seem to help... Open it back up... Then cut some duct tape to hold the art foam down and then tape like you did before.... It may help, it may not. But it will help keep the batteries from shifting and give it a bit more force to hold them inside.