Taylor had the same problem with his Irish measure-topped shot snake. Removed the screw, took the tube off the base and poured in 20 minute epoxy about 1/4" or so deep in the base. The measure now throws 1 1/8oz when set at the lowest throw, instead of 1 1/2oz. You cannot trust the stricken measure with any shot size. I suspect the English measure is no more accurate.
A straight tube (English Measure) can have a shim soldered inside rather easily, reducing the capacity. I'd not use paper, the easiest to install (epoxy) as it will become damp and wet with humidity.
I have a (replica) leather covered Dixon Flask that I compressed the nossel on beneath 3 drams and it throws exactly 3 drams. According to the chart I have, 3 drams stricken measure is just barely over 1 1/8oz. A 1" sheet of brass shim stock, curled and soldered inside might reduce that to 1oz.
In my flint 20, I use that flask with shot and throw the 1 1/8oz, driven by 70gr. of powder. It dusts birds just fine. 70gr. is roughly 2 5/8drams. 68gr. is 2 1/2 drams, 75gr. is 2 3/4 drams, 20 bore loads.