>> "In order to use the find product keys am I expected to upgrade to a basic account at nearly triple the cost?"
Yes, if you're using the API key from multiple machines you'll need a separate user for each of those uses.
Since you're on the Solo plan it's probably not necessary to automate "finding pkeys" for customers (you might get 1 or 2 requests -- not worth the effort of designing and securing such a service).
>> "When they try to reuse their product key on the same computer, they are unable to activate because the product key has already been used"
That isn't likely. TurboActivate correctly handles re-activating the same product key on the same machine without any intervention from you.
If you're using the latest version of TurboActivate then customers that claim that is happening are lying to you. If you're not using the latest version of TurboActivate, then do that.