Your approach to uncheck items that you have put in your basket is exactly what i practise with my shopping list in ‚notes‘ on my phone.
Your approach to use two lists is exactly what I would like to have.
I like your idea and I just like to let you know that. 
If you see an easy way to use your idea without deep custom css knowledge, please do not hesitate to share it here with us tech-ignorant folks 
Nevertheless enjoy your solution!!!