Heavy bullets not necessary. Two loads of mine
One load that works in every .223 I've ever tried it in, regardless of barrel twist, is any 52 or 53 grain match bullet, CCI primers, 26.5gr 748, in Winchester brass. If a rifle will not shoot well with this, it won't shoot with anything. So long as other bands of brass weigh about the same, you can substitute here. This load is somewhat wind sensitive beyond 100 yards.
In 1:7 twist AR's, the best I've found is 69 Sierra or 68 Hornady bullets, Winchester primers, 24.3gr IMR 4895, Winchester brass. This will shoot groups about 1.25" at 200 yards through a match-prep'ed AR.
I have no experience with Mini 14's.
Study your head postitioning with respect to the rear sight when studying AR grouping ability. With AR's it is particularly difficult to get your head in the same location and position for each shot. With the M14 and M1 I was always able to achieve consistent head postion through wrapping my right thumb over the wrist of the stock and putting my cheek bone on top of it (it hurt a little and I got a small cheek and lip bruise but that's a small price to pay). With AR's, consistent head positioning is only achievable through putting the left knob of the charging handle in your right nostril (or something similar), then holding your head at the same angle. It sounds more difficult than it is. If you don't have a handguard float tube, you need to be consistent about sling tension.
Regards,
CDD