I want to create a restriction on a shipping method that it can only be used 1 hour after the most recent use by a customer.
You could do this by hooking into the class
Magento\Shipping\Model\Shipping class's collectRates() function
Just store in a database somewhere or something when a customer uses it, then compare that (plus one hour) to the current timestamp.
If the current timestamp is bigger, then show the method.