There are a number of Ithaca serial number chronologies around. The best is in the Second Edition of Walter's book. Even at that guns languished in inventory for years, even over a decade, as this invoice Walter showed us of guns with 1929-30 serial numbers that didn't ship until 1942.
Them graded guns didn't move very fast during The Great Depression. I have a fully optioned No. 4E 20-gauge in the same 457xxx serial number range as these guns. Walter gave me the info on it and it sold in 1933.
Likewise I have copies of the sheets Roe Clark used when he tabulated the graded Ansley H. Fox 20-gauge guns for McIntosh's book. He did fifty serial numbers per page and there are pages that have guns that shipped from 1928 to 1945 on them.
I'd guess that for several years after the NID came out Ithaca Gun Co. was liquidating Flues Models from inventory at discounted prices to big jobbers like J.L. Galef, etc.