Just trying a couple weights of quality ammo first could shrink your group. And you could find boattails better beyond 200 yards. There is nothing wrong with good factory ammo. Hornady Superperformance can outperform reloads at times. When I got my first custom barrel 223 wylde I purchased 40, 40, 50, 52, 55, 60, 62, 65, 68, 69, 75, and 77 grain ammo including the Sierra Gold match HPBTs. For 100 and 200 yards I shot the BH 52 grn match ammo best, or I should say the rifle liked it best. The manufacturer said for 500 yards to use Federal Sierra Gold HPBT. at 69 grns guarranteed sub MOA. That is if you are good enough to let the barrel do it's thing.

Cheap optics is relative. You can get nice optics ( Nikon, Weaver, Vortex) for $200-300 range now, at least in the 3-9 power range. There are guys who spend $1500-2000 for their optics.

I have shot sub MOA at 200 yards using a $79 Simmon (6-18x50) that I got on sale for $59. Not nearly as nice as my Nikon, but I am old and needed the extra power to see where the bullets were hitting. Of course that was with low wind at my back. Wind is what seperates the great shooters from those of us who try. Now if your cheap optics was the Bushnell Banner, you can do much better. The Savages that come with the Nikons are good to go.

But I was using Black Hills reloaded Match ammo, not boattail but more accurate at 100-200 yards than the boats. Savages are by far the most accurate rifles out of the box.