Nik
You have an example of the .303" Martini Enfield Mk.1 rifle; albeit missing its handguard (which is commonplace BTW as they were prone to splitting). Your interpretation of the conversion of that rifle from MH Mk.111 to ME is correct. The "Arrow S" struck over NZ (New Zealand) on the top of the action indicates the rifle was sold out of service at the end of it's service life. If you could illustrate the rifle's butt disc, we may get some more details of its service.
Many years ago, I used .303" MF ammunition from the 1950's in a ME Mk.1 with no problems. I must say that the ME was not as comfortable to use as an MLE; doubtless because I favored the latter.
Getting meaningful results from your ME depends on the condition of the bore. No point expecting much from a rusted out bore. Unfortunately, here in OZ, many MEs are found with neglected bores - due to lack of cleaning after an owner used corrosively primed military ammunition. If you have a handy gunsmith, a check of the rifle's headspace would be prudent.
These Martini actioned .303" rifles were certainly used in the ABW. Murray (Australian contingents) gives examples of Colonial Australian contingents leaving these shores with ME rifles. Once in SA, however, MLEs would have been issued. Running a sharp eye over group photos of Town Guard and irregular units on this site can show examples of both MH and ME rifles.
Regards
IL.