Jafo, I did some looking and from what I can tell the M&P15OR (optics ready) has an m4 profile barrel, its thin under the handguards and thicker after the gas block.
Ive got a Bushmaster Patrolmans Carbine with the same profile and a 5.56 chamber its chrome lined and MP tested and shoots match ammo like remington premier77gr SMK or Black Hills 77gr OTM (SMK), or the 75gr offerings from Hornady at a 2moa avg some smaller groups and some larger but overall with match its a 2moa gun, with standard ball thats where it gets interesting, I got 2k 55gr Federal FMJBT rounds with the gun and that is pretty consistent at 2.5-2.75" but have had some real good 2-2.5 moa groups with 62gr Lake city and some awful 3"+ groups with other surplus 62gr rounds from who knows where,
So even with handloads I wouldnt expect tack driving accuracy.
The best thing you could do is replace the factory trigger with anything else, there are "Enhanced mil spec" triggers that are really smooth/crisp but are still heavy pulls 5lbs+ for $60-80, they take standard milspec triggers and smooth the engagement surfaces to take the creep out.
Or "standard" type triggers that are designed like the mil spec ones just with better machining and lighter springs that have 3-5lb pulls and crisp breaks for about $120
And complete drop in units from Timney or Giessle with 3-5lb breaks for $200-300. For a carbine Id go with the "enhanced mil spec" or "standard" type with a 4-5lb pull.
Also getting a new handguard that only mounts to the original barrel nut will help with harmonics, they are pretty easy to install and only require you taking off the gas block. as of now anything touching the handguard will also be touching the barrel in two places, the gas block and barrel nut. and with that comes all the inconsistency in harmonics, even when using a bipod.
Probably the best option, and what I eventually went with after trying to turn a 16"carbine into an SPR, Is to buy a new Upper with a Match grade medium or heavy profile 18-20" barrel. That will give you the most gain for the least amount of money.
Say you did spend $250 on the best Timney trigger and another $250 on the best Midwest Industries handguard, you still have a 16" skinny m4 profile barrel. so after $500+ dollars your weak link is still the barrel. and you may only see .25moa better after all that. Thats what I did and thats what I saw, not to mention the ammo I burned, trying this load or that bullet and this manufacturer, I probably spent a good $300 on factory match grade ammo before I finally admitted it wasnt going to get any better. I did sell my handguard and get most of the money back and just run a Magpul MOE one now for the super light weight. But no matter how you look at it I lost a good chunk of cash trying to turn a 16" Carbine into a SPR
A new upper with an appropriately contoured and accurate barrel and handguard will run you anywhere from $600 to $1800 for the super expensive ones.
I spent $625 shipped (on sale i thinks its like $700 normally) on a Rock River 18" heavy contour match grade upper. I get a 1moa avg with factory match loads. I see quite a few .75" groups as well and when the planets aligned I got ONE .6" group with Black Hills red box 77gr OTM and shot the other 45rds at the avg 1moa I see from that upper.
So now Ive got my super accurate upper with a proper scope on it for long range, and when I want to have some fun up close I use my 16" upper with an aimpoint. and I am a stripped lower away from having two complete guns. A far better value no matter how you skin that......potato