Since it's known to be a 72, that narrows it down. I find a CMD code for a 72 Monte Carlo 350-165hp w/TH350 N.B.2 (California). Sequence number has too many digits, should only be 6 - probably 574333 (or you have 1 too many '3s').
Muncie casting number generally fit a range of years.
3846429 ~ 1963 - 1965 Regular thick web, driver speedometer, 27 spline
3851325 ~ 1964 - 1965 7/8" Bore Patent Pending Mostly 1964
If the transmission is anywhere near original, even though it's a wide ratio the gears are different ratio than 66 and later; 2.56 1st, 1.91 2nd, 1.48 3rd, and 1.1 4th of course. Reverse is also 3.16 as opposed to 3.11. Good ratio for getting a heavy car with a high rear end gear going.
See http://www.chevellestuff.com/qd/muncie.htm and http://www.chevellestuff.com/qd/muncie_casting_numbers.htm.