The M1917 receiver will have Eddystone stamped on the top of the front receiver ring. The P14 will have an oval with an E stamped inside the oval with a R and an A like ERA
The bolt face for the P14 will be flat, the M1917 will have a cone faced barrel.
“The gunsmith doesn't have go or no-go gauges?”
“My first thought was .308 but other than taking it to a gunsmith I'm not sure how to tell for sure. Any ideas?”
Yes, I am sure the gunsmith has a head space gage, some have to order the gage when demand presents itself.