You're in the UK? Baugher's has the serial number as 11945, your fuselage frame number should be 11772. He also has your registration as G-AIIH. What does the Data Card say about it? If it's an H Model in 1944, it's a safe bet it was an Artillery Air OP bird. Like mine. It's 82 units before mine, so it could have gone anywhere. When did Ken say it got to Bristol? First Army had already gone over by the time mine got there in July, so mine went to 9th, which was just starting to get fitted out. Mine ended up in a Depot until November when it was assigned to the 407th FA Gp, which was a non- divisional group. Knowing how the army works, it was probably part of a block of airplanes assigned to 9th as they came in, until 9th's allotment of 300 and some plus spares had been filled, then they started outfitting other outfits. Mine was in storage at Villacoblay for most of the summer. You can figure it took awhile to amass over 350 airplanes at the rate they were coming over, so yours may have been part of that allotment as well. 3rd Army hadn't been committed to combat yet, and they had been outifitted long before then, so chances are it wasn't under Patton. I would say there's a better than average chance it was 9th Army.
All this is speculation, and it doesn't help you nail down the unit codes, but it could be a start. The biggest collection of unsearched photos is at Carlisle, Pa at the Army War College. I wish I could get up there to look. I would love to find a shot of mine.