I suspect that if the Australians needed some P14s to convert to "T" spec. in wartime, they would convert Remingtons just as happily as Winchesters. The original selection of Winchesters for conversion is a bit of a mystery to me, since AFAWK there was no inherent superiority in their product over Remington Illion and as is pointed out in "The U.S. Enfield" by I.D.S., the American Expeditionary Force actually requested that no further Winchester rifles be sent to Francein 1918, reportedly due to problems with interchangeability of parts. From how American militiary procurement worked at the time, that could have been nothing but politics, but that's what the record says.
That's not to say that they did convert any RE rifles, only that in the absence of reliable records I wouldn't assume that they didn't just because the War Office specified Winchesters originally. On the other hand, after the various "fast ones" that Winchester tried to pull on the Britishgovernment with the P14 contracts, you'd think they wouldn't have specified Winchester without a good reason!
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