Alright. I will show all of my work.
Initially, I was interested in the Allegheny. With its absurd weight and low tractive effort it is a prime candidate for having boiler pressure increased. It has been said that the boiler was designed for 260 PSI and increasing would required thickening the steel and adding weight, but I wanted to confirm for myself.
In the following link is the 1923 ASME locomotive boiler code.
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwje2Z_MuoaEAxXEEVkFHSPHD6g4ChAWegQIChAB&url=https%3A%2F%2Fasmedigitalcollection.asme.org%2Ffluidsengineering%2Farticlepdf%2Fdoi%2F10.1115%2F1.4058068%2F7067075%2F1033_1.pdf&usg=AOvVaw1HfVvBqVkxlnC_yiKLO5A&opi=89978449
point L21 gives the relevant formula for the maximum working pressure on the shell of a boiler.
P=(T.S. * t * E)/(R*FS)
where
T.S. is tensile strength. L11 gives this as 55,000 PSI.
t is thickness of steel
E is the efficency of the boiler seams
R is the internal radius of the boiler course
and F. S. is the factor of safety.
I initially calculated this with a factor of safety of 4. Allegheny has 3 courses (I will put all the variables in a chart at the end of this.) and the max pressure was 310 PSI for course 1 and 300 for 2 and 3. Holy cow. Looks like the Allegheny was designed as a 300 PSI engine from the get go.
However, looking at L20 of that boiler code specifies that new boilers need a factor of safety of 4.5, and that the working pressure specified by that safety factor cannot be raised above that number later in service. With a safety factor of 4.5 the Allegheny has a max pressure rating of 266 PSI. In line with reality.
To confirm this, I checked against Big Boy and the second run of N&W A's (the ones that abandoned the nickel steel boiler plate), two locomotives that I knew had 300 PSI boilers. Big Boy indeed does have a 300 PSI boiler with a factor of safety of 4.5.
For the A I calculated a 264 PSI boiler with a factor of safety of 4.5, and 295 PSI with a factor of safety of 4. full disclosure, this may be slightly off as the arragement diagram that I had was for the first run and the boiler radiuses may be slightly different. I will get the correct radiuses tomorrow from the N&WHS.
So to confirm this, I went and got the relevant information from the Y6a, the first Y6 to abandon the nickel steel boiler plates. Again, with a factor of safety of 4 the PSI is 300, and with a factor of safety of 4.5 we are looking at a 265 PSI max engine.
Here are all the calculations in a convienent table.
T.S=55000 
Allegheny 


Big Boy 
A (12101234) 


Y6a 




course 1 
course 2 
course 3 
course 
course 1 
course 2 
course 3 
course 1 
course 2 
course 3 
course 4 
Thickness 
1.28125 
1.3125 
1.34375 
1.375 
1.125 
1.125 
1.21875 
1.15625 
1.1875 
1.21875 
1.21875 
seam efficency 
0.861 
0.861 
0.861 
0.925 
0.925 
0.925 
0.913 
0.925 
0.911 
0.919 
0.919 
inside radius 
49 
51.84375 
53.15625 
51.90625 
45.5 
46.625 
51.53125 
46.1875 
48.5 
49.6875 
50.90625 
F. S. 4 
309.5591518 
299.7151899 
299.2746914 
336.9205298 
314.4745879 
306.8867292 
296.9049424 
318.3990189 
306.6994201 
309.9457547 
302.5253223 
F. S. 4.5 
275.1636905 
266.4135021 
266.0219479 
299.4849154 
279.532967 
272.7882038 
263.9155043 
283.0213502 
272.6217068 
275.5073375 
268.9113976 
and some notes.
1. my source for the Allegheny (The Allegheny, Limas Finest by Gene Huddlestonand Tom Dixon) gives just one seam efficency so some of these numbers may be slightly off.
2.Don't have good details on the Big Boy. What I could gather was from this link https://www.railwayage.com/wpcontent/uploads/2023/11/RailwayAge1941UPBigBoy.pdf . I also dont have a seam efficency, just a type (Sawtooth), which per ASME gives between .92 and .94 efficency.
3. I purchased the information on boiler thickness and seam efficency from the Norfolk and Western Historical Society, which is why those results are the most detailed. The following are the exact drawings:
B45779 Y6A boiler bill of materials
B38575 A (12101234) boiler bill of materials
B36044 Y6A boiler seams
B38682 A (12101224) boiler seams
J35974 Y6A logitudinal boiler section
And the A boiler section is on the wikipedia page. Again it may be slightly off.
4. B45779 specifies that the material is carbon steel per American Association of Railroads M115. Per the below link this has a min tensile strength of 55,000 PSI, matching the ASME Spec.
In conclusion, it looks like the N&W was playing to a different set of rules than at least the C&O and UP. Very specifically for the C&O they could have either made the boiler thinner to support 260 PSI, reducing the weight and dodging that issue. Or they could have made a 300 PSI engine with 127,167 pounds tractive effort and a factor of adhesion of 4.00, which when adding a Franklin E booster as it was designed to accept without modification would have resulted in a starting tractive effort of 148,142 PSI, out pulling DMIR Yellowstones and Big Boy at the low end and then crushing them with even greater horsepower at the high end and being indisputably the most powerful locomotive ever by a substantial margin.
But, this leads back to the OG question with a bit of a twist. Was 4.5 or 4.0 leagally enforced. Because if it was 4.5 it looks like the N&W was breaking the law.