Robert, I don't recall seeing any source specifying which flags Hays' brigade captured while researching my books "Lee's Tigers" (LSU Press, 1987) and "Cemetery Hill: The Struggle for the High Ground, July 1-3, 1863" (Da Capo Press, 2003). Hays' comment on capturing four stands of colors might not be a reference just to the Louisiana brigade, but he may also be including some flags taken by the 6th, 21st, or 57th North Carolina since they took part in the attack and he was in overall command. The Tarheels did shoot down 3 colorbearers of the 54th New York and pushed the regiment back, so it's possible they captured that flag. You might try looking at sources on their role in the battle. The Confederates also shot the 107th Ohio's color bearer but a Yankee lieutenant claimed he picked them up and saved them.
Also, I wonder if Hays might be including artillery guidons in the flag count. His men did briefly capture Rickett and Wiedrich's batteries and a Confederate did pick up Rickett's guidon, but had it snatched away by a Yankee. The guidon staff was then splintered by a shot and the Yankee killed. The guidon may have been picked up by the Tigers.
The Union regiments which Hays engaged were the 107th, 25th, and 75th Ohio; 17th Conn.; 153rd Penn.; 33rd Mass.; and 68th, 54th, and 41st New York. A good source to check for these units is David L. Ladd and Audrey J. Ladd, eds., The Bachelder Papers: Gettysburg in Their Own Words (Morningside, 1994).
You mention the letter by Lt. Joseph Jackson of the 8th La. Was that a typo for the date of publication--1863? Not 1963? The original is at LSU and I published it in Civil War Times Illustrated years ago. Also, just a correction. The battle at Rappahannock Station was on November 7,1863. Good luck with your research. Terry