Based on a Remington Society Of America article I read a few years ago but can't find production went as follows:

Eddystone continued production until Dec 30 1918 then ceased operations completely.

Remington continued production until Feb 1919 for the same reason as Winchester, then rolled production over into the Model 30 which continued with various modifications until 1940. It was Remington's first commercial bolt action rifle and sold with great success.

Winchester continued production until April 1919 with the thinking that it would be adopted to replace the 1903 due to it's more robust construction and accuracy. It never happened so with modifications it went into production as the models 51 & 54 and with more modifications in 1936 it became the Model 70.

You will find more post war production Winchesters but the Remingtons are not unheard of. I have a Winchester with a 12/18 barrel date and a serial number of 507xxxx. With a serial number that high I would approximate yours was made in Feb 1919.

By never having seen service most of the post war made rifles I have seen have excellent bores and are great shooters regardless of their configuration. Bill