Do all A bodies have overheating problems?

If it works over 30 mph, then the cooling system is adequate.Your problem is all in the moving air thru the rad when stopped or under 30 mph. That points squarely at the fan,it's drive ratio,the shroud, and . with a possible aggravation if the carb is sucking hot underhood air.

I run;
The fan I use is a 7-blade hi-attack unit off a 73 Dart 318 with A/C. The blades are the biggest widest most pitched I have ever seen. I run it with a thermostatic clutch,( NOT the Mopar viscous coupler) off an early 2000s F150. And I run the 73 shroud, with the fan well into it. I run a slight underdrive ratio on mine cuz I wind it out to 7000 all the time.I run 50/50 antifreeze.And I moved the front Liscence plate way over to one side, and removed the OEM plate bracket(68 Barracuda.) I also run that same 1973 A/C Dart rad. Hyup,44 years old this year.And I run fresh cold air into the 750DP.With these parts installed, my approximate 420 hp 367 runs a solid 205 all the time. I am so confident in the system that I run a 7 psi cap, and have since 2002ish
>I had no luck with the OEM type 6 narrow-blade fan nor the 5 blader with the very wide blades, nor a flex-fan that I tried (that was the worst).

IMO;Your timings are fine, and so is the hi-flo pump/stat (I run those same items).
Have you verified your gauge readings with an IR gun?
You're not running an A/C condenser up front are you?

I had a 69 340-4gear FormulaS, with the totally stock cooling system. It ran fine.As did my 74 DartSport 360 4-gear.And my 70 Swinger340-4 gear. And every other Mopar I ever had, since 1970. The factory systems always got the job done.
So, please don't put all Mopes into the same category as your unit.