In the 9.3x62 in once fired Lapua cases, I loaded up to 62 grains RL-15.5 under the Lapua 285gr Mega, and 64 grains under the Nosler 250 AB, both bullets at 3.375" COAL. Here is what the case fill looked like with my little 4" RCBS drop tube.
[Linked Image from i.postimg.cc]
[Linked Image from i.postimg.cc]
The 285 Mega seated perfectly, since it's a short bullet, and the base just snugged right up to the 62 grain charge
[Linked Image from i.postimg.cc]
The 250 AB required some decent compression but seated fine. Both it and the 286 PT extend below the case shoulder at 3.375"
[Linked Image from i.postimg.cc]
I cobbled up an 18" aluminum drop tube and dropped the same 64 grain charge as pictured above with the 250 AB, and it definitely helped. It makes the 64 grain charge look closer to the original 62 grain charge pictured above with the 285 Mega.
[Linked Image from i.postimg.cc]
So bulk is an issue, but I think I'm going to be fine in my rifle, with the 3.4" magazine and long throat. That long throat is standard for most all 9.3x62s so RL-15.5 may be a player for this cartridge.
I will follow up with the loading bulk for the .338-06.
From prior testing, I know that my 35 Whelen AI cases have about 0.3 grains of water more capacity than my 9.3x62, when both are filled to the base of a 250 grain bullet seated 3.375", so I am hopeful for that chambering as well.

Cheers,
Rex