Welcome Daniel,
On May 1, all the permits that people won, but did not pay for, are released back to the online system. They are released at random times throughout the day, so set up a bookmark and check it often. You may find something you want.
The first post in the Lottery thread has links to both the day hike reservations and the overnight ones.
If you don't get permits that way, you are left with coming out and trying for easy-to-get walk-in permits. There are always no-show people, so people can always get them. Unfortunately for you, it is tough to come from so far away and count on getting lucky. If you google Unused Whitney Permits, you can see the numbers for the past years.