You're right. After reading your post, I recounted (this time taking off my shoes). And since this time I did NOT include a June 31st, I also came up with the 5th. :-)
So flags should indeed still be at half staff on July 4th.
Here's another government site:
http://www.usda.gov/oo/beprepared/Reaganflags.htm
"The following information was provided by the U.S. Department of Homeland Security, Bureau of Immigration and Customs Enforcement, Federal Protective Service, National Capital Region.
Date: June 05th, 2004
To: All Regions and Federal Agencies
From: Suitland MegaCenter, National Capital Region
Subject: Occasion to Half-Staff the American Flag
Due to the death of our 40th President Ronald Reagan on June 5th 2004, the American flag will be flown at Half-Staff in accordance with Presidential Proclamation 3044, as amended (see Federal Protective Service Uniformed Force Operations Manual PBS P 5930. 17A, Chapter 22).
In accordance with the special Presidential Proclamation, the American Flag will be flown at Half-Staff for the following reason(s): in honor and tribute to the memory of Ronald Reagan, and as an expression of public sorrow.
The American Flag will be flown at Half-Staff for 30 days to begin immediately. On July 5th, the flag will go back to full staff."