Circled P without serifs and small ordnance wheel?

[RCS]

The original Winchester circled P stamp has the serifs. The second P proof stamp can be either a non serif P or a serif P stamp depending on the time/place of rebuild. The small crossed cannon stamp started with the later SA EMcF stocks, SA GAW, SA NFR and original SA SHM stocks - it is located on the top of the pistol grip and is not a rebuild stamp.

Photos show an early Winchester stock with the original P proof with serif and a second firing proof with the non serif P. Second photo shows a Winchester stock with both original and second proofs with serifs. Your RIA EB is a post WW2 rebuild stamp