Grand Island hotels are slim pickings anyway.... I've stayed at the Best Western there a couple of times (which is also the crew hotel for Great Lakes if I recall correctly) and it's pretty scary.
Something big must be going on in Grand Island... all like 8 or 9 hotels are sold out.
I'd advise looking nearby.. might be a small drive, but I'd look for hotels in Hastings. It's only about 25 miles from Grand Island (to the south, down US 34 if my memory is right) and is showing hotel availability for those dates. It's probably your best bet.