I agree with Naki, except that if it were me I would do everything I could to avoid a re-bore/rechamber as this would then require a re-proof and IMHO would affect the value of the rifle. If .308 bulets require a light tap to go down the bore, then the first step would be to get the bore measured to see if there are high and low spots. If there are, then fire lapping may be the answer and then shooting with .312 bullets or whatever matches the bore measurements. I agree that recrowning would be a good idea. If there are considerable variations in the bore measurements, then more lapping may be needed to even this out (to a achieve a light taper from chamber to muzzle). However, if after this process the measurements suggest that a .318 or .323 bullet would be better, you need to consider the chamber neck dimensions to avoid excess pressure (you can't just load a .303 case with a .323 bullet if the chamber neck is too tight).
I'd get an expert to measure the bore first and decide where to go from there. Overall it looks a nice gun and a fun project!