The 1960 vintage .243 Sako L579 I recently bought has shot most bullets I've tried very well. (85 gr Speer BTSP, 85 gr Nosler Partition, 95 gr Fusion) I think the twist is 1/10.
I've found the powder selection makes more of a difference in accuracy in this rifle than bullets do. I'm getting consistent sub MOA accuracy using H4831SC, IMR4350 and H335 with the above-mentioned bullets, even the Partitions.
This rifle does not shoot loads well that use Varget powder.
Another thought - It might pay to check rings and bases too.
Good luck in your quest.