I think filling the case is somewhat overrated.

Using H4198 in a 308 (Rem. 700 VTR) with 155 grain bullets I've developed a very mild shooting "30-30" that prints 1/2 to 5/8 MOA five shot groups. And I mean all the time, not just it did it once. This is with thrown charges, and they don't fill the case. But there is not enough room for a double charge either.

I'm pretty certain a similar mild and accurate load could be developed for the 300 using 4198.