Jack, I'm sorry I forgot to give you an accuracy improving tip for your P14.
Check the wood to metal fit at the front band. If you can move the barrel up and down, that is the front barrel band is not in contact with the barrel there is a remedy. This is a critical spot for accuracy with these rifles. They actually had a fixture that measured the upward pressure on the barrel in pounds when these rifles were built. The P14/M1917 series rifles are designed this way. If it is loose the rifle will always shoot badly. After 102 years the wood tends to dry out and shrink. The remedy is to shim the barrel directly under it's centerline the length of the barrel band. There should be no other contact of the barrel and the stock between this point and the chamber. Find yourself some stable older wood to make the shim from, Walnut is preferred. Years ago I purchased a $5 beat-up cut down M1917 stock at a gun show just for this purpose. It doesn't have to be super tight just enough so that the front band is in contact with the barrel. You should be able to get the front band off with a little effort.
It doesn't seem like much but this little trick closed up the groups on my P14 by nearly a 1/2" and my M1917 by a 1/4". It all depends on how loose the fit was to begin with. I hope this can help with your accuracy issue as a P14 should shoot better than a 3-5" group. - Bill