I realize that we are now heading off on a tangent from the FB Mk VI. My apologies, but I just love the history of this airplane.
Sharp & Bowyer as well as Bowman (Wings of Fame Vol 18) state that only 20 B Mk IVs were modified to carry the cookie. These airplanes used Merlin 21 or 23 motors.
The B Mk IX was a progression/variation of the PR Mk IX with Merlin 71/72 or 76/77 motors (as you alluded to). Only 54 B Mk IXs were delivered, all between April and November of 1943. I have not come across a definitive number that could carry the cookie. Bowman again in WoF Volume 18 on page 59 writes "a handful" were modified.
The B Mk XVI was a progression/variation of the PR Mk XVI with Merlin 72/73 or 76/77 motors. Total deliveries between and November 1943 through May 1945 (~VE Day) was 356 based upon the delivery charts by Sharp & Bowyer. I don't have a definitive number of airplanes that could carry the cookie.
WRT the Packard-Merlin powered Canadian built B Mk XX and B Mk XXV, I'm uncertain if they were modified.
Edit: From Sharp & Bowyer's Mosquito page 106, only five B Mk XXVs (KB409, 416, 490, 561, 625) received the bulged bomb bay doors. These few went to No. 627 Sqn according to the text on page 104. Apparently 8 Group had pushed to get their Canadian built aircraft modified with the bulged doors, but Pathfinder gear caused a CG problem that would require re-fit with different motors. Considering the logistics problems getting spares for Canadian built airplanes, the plan was abandoned.