I can't start this until June as the " going to the sun " road is closed until 21 June.
I agree that waiting for GTTS Road to open is a great idea. Your trip would be missing something special if you cannot do it. However, I must warn you that it doesn't have a fixed opening date as you have implied. The NPS has announced that the earliest possible
opening date in 2014 is June 20. Over the last 14 years, GTTS road has been open by June 21 exactly half of those years, 7 times. Only two of those 14 years, however, has the opening been past June 28. In 2011, it didn't open until July 13.
I would suggest monitoring the snow reports to see how much snow Glacier gets this winter. If the snow is heavy, you might consider pushing your starting date out far enough so that you don't get to Glacier too soon. It's a bit less than 800 miles from Anacortes to the base of GTTS Road, so it will take you about two weeks to get there. You also need to monitor the status of Washington Pass, which you will encounter in the first few days out of Anacortes.