I have a good amount of experience on a bolt gun and a gas gun but admittedly probably not enough. I have tried 175 smk, 168 hornady and the 178's. The gun is factory with a Harris bipod and I use a bag in the rear. Most likely it is operator error. I have a Nikon monarch scope 4-16 and I am switching to a vortex pst soon. Iam sure the Nikon is fine I just want a FFP. I have to accept the weight and get more training from what I gather.
Well...that's not exactly what I said, but certainly, depending on your experience and skill-set with a semi-auto, some specific training on running a large-frame gasser properly is NEVER a bad idea. As for the weight...again, there may be room to shave some weight, especially with different stocks, grips, mounts/rings (depending on what you are running now), etc., but the basic 9lb weight of a stock POF P-308 with a 20" tube isn't really going to get trimmed down much, so you are generally correct that you should probably learn to live with the weight and, if you want something lighter and/or more portable/maneuverable, then build or buy with those objectives in mind from the get go in lieu of trying to mod the P-308 into something that it really was never meant to be in terms of weight.
Now, back to accuracy woes...
You said that you have "tried 175 smk, 168 hornady and the 178's" but that doesn't say a lot. Are these your reloads (if so, are you loading specifically for a semi-auto or running the stuff you'd just normally run in your bolt guns...what's your reloading procedure...are you crimping or otherwise ensuring that you have adequate tension on the bullets and that you aren't getting any set-back, etc. when the ammo is rattling around in the mag or upon chambering, etc.)? Is the ammo factory-loaded match fodder? etc.
Also, you noted your scope selection, but said nothing on your rings or mount. What are you setup for in those areas (make/model/etc.)? Are you properly installing everything in terms of per the mfg's instructions on torquing of the cap screws and mounting screws (or levers if a QD mount)?
How does the rifle "fit" you? Are you getting setup on it properly? How's your cheek weld (I ask bc the POF's rail is somewhat higher than a stnd large-frame AR to accommodate the piston operation which causes your optics to sit higher and depending on the stock you are running, you may have a chin-weld instead of a cheek weld or otherwise not be getting a good, solid, consistent setup on the rifle if your scope is mounted too high...back to your ring/mount combo)? Also, are you loading your bipod properly? Have you tried removing the bipod and shooting from a rest or bags?
Have you let anyone else, particularly any known semi-auto shooters, fire the rifle to remove any possibility that "its just you" causing the issues?
Just some food for thought.
If you can eliminate all the "external" factors, and you are still having issues with poor accuracy, then it may be time to call POF and inquire about an inspection and possible repair of your rifle as it wouldn't be the first time that one wasn't shooting well. If it is something wrong with the rifle itself, they'll take care of you, but before you get to that step...its best to eliminate the above factors, try some different ammo, etc. because they'll want to know on what you are basing the fact that your rifle "won't shoot" before you bother with shipping it in for evaluation.