You should have no problem putting in those days.
Here's how you reserve permits:
Current availability on recreation.gov for late May (EP 38)If EP 38 fills up and you haven't reserved yet, you can go next door to EP 37 Kawishiwi Lake. Lots of permits at that EP, also (14 per day?)
---But I would worry that campsites near those EPs may be fairly scarce.
I went into 37 in July 2011, and there was plenty of campsite availability throughout our trip.
The fishing should be great. If the bass haven't warmed up yet, then the pike and walleyes should still be bangin! Should be good for all three species. That area is full of walleye, pike, and smallmouth bass factories. We caught some HUGE smallmouth on the Kawishiwi River. They're STACKED UP in there.
Good luck!