Studio image - convert off-white background to white

Hello all, first time poster (be gentle).

I am following this tutorial: https://www.gimmesomeoven.com/eyedropper-tool-photoshop/ 

My client has sent me lots of images taken using a mini studio and iPhone. The backgrounds are not pure white and I am frantically trying to convert them.

Here's a sample of how the photos look before any editing takes place (Windows folder):

After using the eye-dropper method, I do have some success, but they aren't quite good enough.

Here's how they look on my website after editing:

I really need them ALL to be perfect.

Another issue I'm facing... I'm having to manually choose a dark section of the white background which is very time consuming. I was hoping to automate this and then batch process with an action.

I have searched online and cutting each image out individually simply isn't an option. I have litearlly 100s of photos.

Any advice is MOST welcome.

Thank you.

Antony