The fact that it has the U.S. ordnance bomb indicates that it was either one of the never delivered rifles which was subsequently used as a training rifle or else it was issued during the AEF incursion into Russia after WWI.
I have to say I have seen more Westinghouse rifles than I have Remingtons, and I always felt that the Remington was slightly less common than the Westinghouse, having owned a couple of each over the past decades. One Westinghouse I had in particular had the ordnance bombs and eagle markings, which I foolishly sold off.
I would say $300.00 is a very fair price for that particular rifle as it is part of U.S. history.
One note of warning: Make sure that some clown hasn't rechambered it to .30-06. This was a common practice back in the 60s and 70s to make the rifles more salable, and left the rifles with dangerously oversized chambers.