[Ted51abcdk]

Leendert and all:
Kent is correct about 41-6397. The 62nd FS Mission schedules are exclusively codes only beginning on April 17th, no serial numbers except for the April 13th Mission which is serial numbers only.
I am sad to say that the IARc will not be of any help to you as the last penciled in line records the date of 31 October 1944 with the only preceding date beginning the Depart US date. There are a total of 37 P-47Cs and 21 P-47D-1s that have this end date of 31 October 1944. It is my belief, and I have nothing to back it up, that this was a "catch all" date used to get airframes off inventory that could not be accounted for from any records.
The only potential sources for these early s/ns would be:
Cumulative Losses Listing which started showing P-47 losses in July 1943
Missing Air Crew Reports which also start in July 1943 for ETO P-47 losses
RALDA (Report of Aircraft Lost Damaged Aborting) which starts with ETO P-47 losses in August of 1943
Sadly, all these dates are post April 1943. It would be my opinion that unless there is some undiscovered documentation out there somewhere that you may be out of luck trying to 'discover' what LM-Gs serial number was for 29 April 1943, that day it was lost.
On the upside, your question did cause me to review and correct that error as well as Kent's comments. Hope that this helps a bit. Ted51