James Cahall, it's tough to find someone who will match your available times, and then link up. It is easier to be ready to go, and keep watching the days just ahead of the current day (during the summer) for a slot to appear on recreation.gov. You need to set up a link to the site and permits you want, and keep checking multiple times every day. When one shows up, grab it and go.
Teddimitri: Yes, April 22 at 7 AM a few slots will become available to the fastest/luckiest. But I am not sure how feasible this will be. I tried grabbing a Vehicle Entry pass on March 1 for Glacier N.P., and the website kept saying it was too busy to process my request. I kept trying, finally got in. But that was for 700 slots per day for all of July. The entire month's slots were gone in 30 minutes. I recommend trying to snag a permit as I wrote for James above.
Permits show up on rec.gov whenever any are cancelled (or a party size is reduced), or a permit becomes a no-show. When that happens, the permit is made available "at a random time in the next 24 hours" on rec.gov.