Very limited information available; I'm sure you are already aware of these sources:
For some reason the European users seem to have often referred to the P14 as the "Ross-Enfield" Rifle - I'm not sure if that was a contemporary "Pre-war" description, or a modern affectation.
Latvia
Boys of the Dvina - Latvia's Army 1918-1940
By S. Kiersons, MA
Page 47-48 refer to 40,000 P14s, known locally as the "Ross-Enfield"
Estonia
discussion regarding P14 use and modification into a sniping rifle:
http://images.vfl.ru/ii/1530557218/6...1/22333516.jpg
The Use Of The Mosin Nagant In EstoniaModel 1931 Sniper Rifle
This was an interesting rifle that combined receivers and bolts from BritishP14 rifles and an Estonian made barrel. The magazines were Mosin Nagant in origin. There was a new stock produced for the rifles and the rifles were equipped with Lyman diopter sights. Two calibers of the rifles were produced – 303 Brit and 7.62X54R. Total production was 1,300. Note – it is not known what the ratio 303 British to 54R. This is not really a true Mosin Nagant but still should be mentioned in this section.
look at the pictures, there is a modified P14 in the display case which appears to fit the above description.
Unusual T30 - Finnish or Estonian?
Lithuania
Lithuanian Firearms