Can we expect some of these slots to become available?
Yes, but at random times. May 1 will be the next big day, but those will only be the permits that winners have completely ignored, and have neither declined nor accepted. I am told the number has been significant in previous years. But these permits will go online at random times throughout the day on May 1, the same way other released permits are handled.
A few will randomly become available this month as latecomers logon and a few cancel. Or winners return some of their slots.
So what you should do is set up a bookmark/favorite on your browser, setting it to find the specific type (day or overnight) and the dates you want most. In fact, make it your "home page". Then every time you are online, you can see if any are available with a few clicks. Use the links I provided above, copy them, and then modify the date to what you want (I would set the date to a few days before my target).
I cannot find a way to tell it the group size in a link, so it asks every time.