If you want some fun Brooke, go to this link on the 340th BG website:
That is a good reference, thanks.
All I'm saying is this: there was a significant number of B-25J's at some point between Jan-June, 1944 in XII Bomber Command. So, May is fine.
With regard to your reference, mostly they don't refer to what type of B-25 they were flying. So, seeing the first mention of a B-25 variant doesn't mean that's the first time it was ever used. Also, they say, "The missions listed below are only those for which we have photos of the target." I noticed that when I saw there were missions listed in December 2, 1943 but then next is March 10, 1944.
Here is another site of many pictures of B-25's, specifically of the 340th BG. "B-25 Photos from Charles Cook’s Photo Collection, Edited by his son Doug Cook. . . . These B-25 Bombers were primarily B-25 J Models." Charles Cook was a B-25 pilot in the 340th BG.
https://www.reddog1944.com/340th%20BG%20487th%20BS%20PLANES.htmSome of the B-25J pictures, with mission # and date:
340th BG 487th BS - SN 43-32704 - 7A “MY NAKED ASS”, mission 6, April 13
340th BG 487th BS - SN 43-27656 - 7C "McKinley Jr. High", mission 19, May 19
340th BG 487th BS - SN 43-27556 - 7D, mission 4, April 3
340th BG 487th BS - SN 43-27540 - 7E WATCH COPIER, mission 32, June 6
340th BG 487th BS - SN 43-27510 - 7F WILLIE, mission 1, April 3
340th BG 487th BS - SN 43-27478 - 7J YAHOUDI, mission 29, June 3
and others
So, B-25J's were there in enough numbers that most of the B-25's in a 340th BG pilot's photo collection, that spans from April onward, were J's.