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Somewhere I read how they went about proofing 2” guns when they first came out and later adjusted their method. I’ve seen a couple of 2 inchers that are proofed at 1 1/8. How did they do that ? Where they proofed using 2 1/2” shells to start?

The long version
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The Proof House declared in 1935 that 2" would be proved at the pressure of 2 1/2" (and 2 5/8") guns (standard service with 1 1/8 oz.)
There were three proof load for each of the 3 lengths 1925 to 1954; for mean service and mean proof pressures as follows (from one source):
2 1/2" (and 2 5/8) - 9500 psi; 13,700 psi
2 3/4" (standard service with 1 1/4 oz.) - 10,500 psi; 15,900 psi
3" (standard service with 1 1/2 oz.) - 11,200 psi; 17,300 psi
(Those numbers were derived with crushers (LUP), and 10-14% should be added for modern transducer values)

I have found nothing published suggesting different proof loads for 2 1/2" 7/8 oz. or 1 oz. or 1 1/8 oz.
Bro. Venters has been in contact with the Birmingham Proof House to confirm.

I think the best information we have is from Burrard's The Modern Shotgun, Vol. II "The Cartridge", 1955
Standard load & pressures for 2" cartridges at 7/8 oz. 2.36 Dr. Eq. (26 grains of 33 grain = 3 Dr. Eq. powder) Service 2.25 tons = 6,440 psi; Max. Service 3.0 tons = 8,960 psi.

BTW: his 1947 edition lists a "Low Velocity: 2" load with 2.2 Dr. Eq. (24 grains of a 33 grain powder) and 1 oz. shot. No pressure was provided.
It is possible those 2" guns marked 1 oz. and 1 1/8 oz. were to use the lighter powder load?

The Proof house can use a shot capsule, extending the overall length, in a Proof Cartridge if they cannot cram a Proof load into the standard case for the chamber.

You could clarify this? A 2" chambered gun can't accept a hull longer than 2". Gil

The excess shot could be carried in a paper tube that extends past the case mouth and into the forcing cone.