Sorry to hear about the hassle. A white screen Customizer is usually a plugin conflict or a PHP memory shortage. Start by temporarily deactivating all plugins and test the Customizer, does it fix the issue? If so, reactivate your plugins one by one, test the Customizer after each activation.
Sounds like a memory shortage. Not an uncommon problem in WordPress. You can sort this out yourself if you’re ok working with a bit of code. However, the easiest is to ask your host to make this change for you.