I have the same problem in my site https://www.arcticwarriors.fi which results a) some customer are not able to go to checkout (button does nothing, purging solves this) b) amounts in the cart change all the time.
I have followed your advice from your blospost (wpw-fixing-lscachewoocommerce-conflicts/) and the results are:
1) Finnish Home page (/) and product page do get cached but only after hitting reload.
2) When getting back to home page after adding product to cart, cart shows different
3) English pages (/) do not cache at all. Using WPML for translating.
I have enabled the plugin, until problem is fixed. What should be done?