I have the Remington 700 and it had a 1:9 1/8 twist. The 105gr would not stabilize with that twist. I did somer research and came up with the 90gr Bergeran and it works great. I only looked at the rounds that were currently available a you may or may not know, there is pretty slim pickings on 243 right now.
A lot of people have success with the 105gr BTHP from hornady. I am currently testing it in my factory rem 700 and so far it is working good. But I haven't got it out past 200 yet but it stabilizes at 200. Berger 95gr VLD is a great bullet also and should work great for that twist. I am using H1000 but soon to be switching to H4350 bc of lack of H1000 availability.
I have shot 62gr. To 105 gr Hornady's out to 600 yards with great results. I did not have good accuracy from VLD's either 95 gr. or 105 gr. My shooting buddy shoots 95 gr. VLD's with great accuracy to 600 yards with his Remington 243, 9-1/8 twist, the same as mine. You never know till you try.