I'd find the twist rate of that very barrel.
Then I would look at Lilja barrels twist rate chart, as well as Shilen barrels twist rate chart. Both will tell you the optimum bullet weight (length) for twist rate.
Then I would investigate if IMR-4451 is a good powder for .243. Reason being, H-4350 is not looking like a long term, reliably available powder. IMR-4451 is reported to be a great substitute for H-4350 in 6.5 Creedmoor. I would think it would be a great substitute in .243.
That's what I would do, anyway.
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