Need Advice on a US Model 1917 Eddystone Sporter

Just picked up a US Model 1917 Eddystone rifle that has been sporterized. I have a few questions. Its not a typical sporter, configuration. There is a custom trigger guard and no floor plate, the magazine was recessed into the stock, thus eliminating the floor plate. The barrel is not free floating. But the bore is bright, with very good rifling. It has the rearsenaled High Standard barrel. I have not shot it yet, but the previous owner stated it was accurate. If not, with no trigger guard/plate, how could I pillar bed the action? Or would it be better to glass bed to free float the barrel. Or would it be better to just leave it alone. Its been like this for 20 years or so. I will be getting a new scope and rings soon. I am including some photos. Any input would be helpful.

the square bottom actions work better with standard glass bed free floating, then pillar bedding, with the sporter stock you have pictured, it should shoot better then most can see, if you glass bed and flaot that barrel.
i would possibly update your scope and rings, that in itself will improve your groups.

Is That a sported 1917, or a Remington Model 30? Nice looking piece either way...