Barring any late storms, most of the snow should be gone by late June, and the lakes should be melted (for the most part) by then as well, enough for water supply. I don't think Garnet/1000 Island should be a problem at that time of year, especially midweek.
Here is a good trip report form a trip in June (somewhat of a dry(er) year, if I recall)
<a href="http://www.flickr.com/photos/jhendersonphotography/2666123851/" title="_MG_1808 by jhendersonphotography, on Flickr"><img src="http://farm4.static.flickr.com/3112/2666123851_9bbe1c7c02_o.jpg" width="600" height="400" alt="_MG_1808" /></a>
Taken June 13th 2008
The hike In was about 50 percent snow coverage. I did use crampons in two spots coming in through spooky meadow. Thousand island was frozen in the morning and melted in the eveninig.