Good to know that it's not an issue in your case but just a reminder that your specific case is, by definition, not generalizable. These are problems that exist in general and have to be solved or prevented in some way. For example, you found some solutions that work for you but they won't for everyone.
Stock doesn't matter for my case.
The browser has storage options to handle close and reopens.
Prices in each currency are all in ints (i.e. cents) to avoid float issues.
There are problems to address on either end that you have to be aware of.