The round bolt was intended for new production and then rebuild of M2 carbines. The round bolt was stronger and was suppose to have a different cam action on recoil. When stocks of the flat bolts were used up, then the round bolt was allowed to be used on M1 rebuild.
Actually, round bolts went into production for m1 carbines with various manufacturers @ 1944. I would highly suggest the books War Baby and War Baby Comes Home by Larry Ruth, as a starting point for learning when and how certain modification changes took place and why.
Agree with the date, however my info is still correct ref:
TM 9-1276 Dated Feb 1953; Paragraph 44 'Inspection of Bolts': (i) "Check to assure that only full round bolts 7160092 are used in the carbines M2 and M3 (fig. 58). Bolt 557148 will be used in carbines M1 and M1A1 in so far as practicable in order to conserve supply of bolt 7160092 for use in the carbines M2 and M3."