My first goal with a new rifle is to get it sub-moa. You are already there, but like most of us, you want better groups for those longer shots. Several times I have heard guys in a gunshop say ... "I'm going to shoot such and such a bullet with my new rifle." I think that the rifle should tell us what bullet it likes. This sounds a little elementary but I think it should be said. Even guys I shoot with have a preference to what bullet they want a firearm to shoot before they even fire it. I have never done this because, as we all know, every rifle is different.
My point is I broke my .223 Handi's in on Winchester White Box 45's. Like quick said, 200 rounds or so, and it will more than likely settle down and even be a better shooter. Neither one of my .223's shoot great groups with bullets under 50 gr or over 60 gr. They both shot the WWB sub-moa but were not all that consistent. For my rifles, the best results came from Nosler BT 50 gr and Hornady 55 gr V-MAX bullets. I have a friend who has a better bullet selection (he reloads for 10 calibers or more) than some gunshops so he let me try a variety of bullet weights without me having to buy a box of fifty at a time. This really helps me a lot.
The scope idea is a very good idea too. Good shooting to you.