I'd hesitate to use MkVIIIZ of any manufacture in an SMLE MkIII or earlier rifles. I hear the Australians had forbidden its use in their No.1 Lithgows, and a safety warning from Australia which I found on a European site said some greatly overloaded MkVIIIz bearing a headstamp similar to the Privi Partizan stamp had damaged rifles there.
Metalurgy of the SMLE was not well standardized at the time most were manufactured, with Nickel content varying greatly. Nickel content gives the action body its ability to recover from flexing without permanent stretching.
Some SMLE have as much as 3.5% Nickel (roughly equal to the P-14/M1917)while 2.75% was considered the acceptable lower limit. Those with less nickel may stretch if repeatedly subjected to more than 45,400 CUP of the MkVII ammunition.
From some obscure remarks made by Skenerton some late production Lithgows may have been made of a Carbon Steel alloy with no apreciable nickel or chrome content.