Here is the 2005 list from the original JAWS website, which started listing the schedule shortly before Greg Wong took over as President from Karl Reichert. Please note that August to December is extrapolated backwards, as the schedule wasn't posted or recorded until January 2006.
January 2005:
Azumanga Daioh: Volume 1
.hack//Sign: Login
Last Exile: First Move
February 2005:
Azumanga Daioh: Volume 2
.hack//Sign: Outcast
Last Exile: Positional Play
March 2005:
Azumanga Daioh: Volume 3
.hack//Sign: Gestalt
Last Exile: Discovered Attack
April 2005:
Azumanga Daioh: Volume 4
.hack//Sign: Omnipotence
Last Exile: Breakthrough
May 2005:
Azumanga Daioh: Volume 5
.hack//Sign: Uncovered
Last Exile: Grand Stream
June 2005:
Azumanga Daioh: Volume 6 (FINISHED)
.hack//Sign: Terminus (FINISHED)
Last Exile: Queen Delphine
July 2005:
Last Exile: Sealed Move (FINISHED)
Other titles TBA. Retirement night of President Karl Reichert.
August 2005:
Premiere run of the new President. Titles TBA.
NOTE: When Greg Wong took over, he did two-episode samples of newer shows that were popular: e.g. One Piece. This continued in part for the next couple of months, until we settled into a new schedule – so we would have played these first trial episodes until then.
September 2005:
Shuffle: Eps. 1 & 2
Shingetsutan Tsukihime: Eps. 1 & 2
Elfen Lied: Eps. 1 & 2
October 2005:
Shuffle: Eps. 3 & 4
Shingetsutan Tsukihime: Eps. 3 & 4
Gun X Sword: Eps. 1 & 2
Elfen Lied: Eps. 3 & 4
November 2005:
Futakoi Alternative: Eps. 1 & 2
Hundred Stories: Eps. 1 & 2
Shuffle: Eps. 5 & 6
Shingetsutan Tsukihime: Eps. 5 & 6
Gun X Sword: Eps. 3 & 4
Elfen Lied: Eps. 5 & 6
December 2005:
Futakoi Alternative: Eps. 3 & 4
Hundred Stories: Eps. 3 & 4
Shuffle: Eps. 7 & 8
Shingetsutan Tsukihime: Eps. 7 & 8
Gun X Sword: Eps. 5 & 6
Elfen Lied: Eps. 7 & 8