If the 264th sqaudron has an association, someone might know or might have kept a journal that might have info. The only thing you may have to deal with using journals and memory are that in the heat of combat, things are fast and furious. You could read the combat report from 2 guys that were within arms reach of each other, and hear 2 completely different stories. Neither are necessarily wrong, it's just that there is so much going on for the brain to process, the things get jumbled.
That said, if he went down in the channel after the engagement, one of 3 scenarios are possible. One, he was a straggler that may have been picked off by the roving bands of Luftwaffe pilots looking for stragglers, he was a straggler that didn't make it back due to battle damage. Or three, he was seen as he ditched by one of his squadron mates. If the third, then an association or journal might help. Otherwise, it is lost in history.
If the first option and you can find out what squadron/group was involved in shooting him down, again a journal or journal of a wingman might provide some clues. I enjoy a mystery as much as the next guy, but you may be looking for a particular needle in a stack of needles.