Your second strategy sounds very interesting. Especially because you can A/B test the licensing period and the text that prompt users to register even in people who have been using the trial version for a long time.
However, I don't understand how it helps paying customers.
And this is totally fine. These are the users who consciously decided to run hacked version instead of the original. Why they would do that is beyond me, but I am damn sure I will not ever see a one of them as my customer.
The only drawback is that of that them making a fuss because of the crashes and this is easily mitigated as per above. You just have to keep in mind that checking Referrers in website logs and following up on any product related discussions out there should also be a routine. So for anyone complaining about the crashes - post a link to the support article explain why and when it does that.
> However, I don't understand how it helps paying customers.
Primarily by not needing to spend any time on support/PR issues stemming from the use of hacked versions.