A couple comments on my part might help at this point. First, I really appreciate that you want to get things right - that goes a long way with me.
I need another day or two to sort out all the issues I have found in looking through all the parts books for the various model years but it seems at this point the heater cores for the 69 and 70 C bodies with a/c are not the same as the 71-73 C bodies with a/c. At this juncture though, I do not yet know myself how they are different. I do have a complete heater/ac box out of my 1970 Chrysler 300 that is currently in the body/paint shop (I sent them a rolling shell to work on and took the interior out for example including the heater/ac box). I have another 1971 Chrysler 300 that I am going to also take to my body/paint shop and am near to getting that one ready to also strip to a rolling shell. So I will have its heater/ac core assembly out too in another month or so. Then I can look at them both closely to determine what the differences really are. Also,
@Big_John might already have each of those model year boxes available in the stash he has too. When I am at this point, I can also compare the evaporators too.
Also, the cars on this site are all focused on C bodies, and not on B bodies - there is another site "For B Bodies Only". So the HC 3071 would not apply to our cars at all.
Also, the HC 3070 does not apply to any 1969 and up C bodies but may be correct for the 1965 -1968 C bodies, but since I don't have any of those I can't comment on C bodies before the 1969 model year.
Therefore, at this point the only heater core shown above that would apply to the fuselage C bodies (from 1969-1973) would be the HC5777 core. However, there seems to be some difference between the 1969-1970 fuselage C bodies and the 1971 - 1973 C bodies. Therefore, we need to know how this HC5077 core differs between 1969-1970 models and the 1971-1973 models. Like
@furious70 said, the differences might well be small but significant enough to be a problem for one of those two groups for the heater core/evaporator to properly fit in the fiberglass housings they reside in. For example,
@david hill experienced with
@ayilar's 1970 Chrysler 300 convertible, some significant problems getting the heater core to fit properly when he was changing out the heater core in that box for a new one. We definitely need to get to the bottom of the 1969-1970 models and the 1971-73 models. I do know that one of our members Tim
@sixpkrt did finally get a correct heater core for his 1971 Chrysler New Yorker after sending the first sample you provided to him back to you and you modified it correctly to finally fit. It might well be that your last return was from Tim back in September of 2021 but I am not sure and it may well be that no one knows at this time what was done to make it fit (maybe Tim knows)?