I would get a 8x68S without one second of hesitation...
Of course, Americans will favor the .338 Win, probably because they know it better, and that is OK, but the 8x68S (S for August Schüler), is a mighty round. Its American equivalent would have been the 8 Rem Mag, if the caliber had taken off, which it never really did, and it is a lasting shame...
There are three good rational reasons to go for the 8x68S,
Willem le Clus...
Filling the gap...
You already have a .25, and a good one at that, with the .25-06. With bullets from 5.5 g (85 gr) to 7.8 g (120 gr), this takes care of all small and medium PG out to as far as you care to shoot. I admire and share the 300 m self-imposed limitation. This is hunting after all, not sniping or target shooting at live animals...
You also have a .375. OK, I would prefer the H&H, for ammo availability, but the Ruger works. With bullets from 16.2 g (250 g) to 22.6 g (350 gr) This takes care of the DG.
Eliminating the 7x57 from the discussion - it is your son's rifle - what you miss is a heavy PG rifle (e.g. Zebra, Hartebeest, Kudu, etc.).
The middle of the caliber gap between .25 and .375 would be .312. The 8 mm (.323) is closer than the .338, and, frankly, the 9.3 (.366) is so close to the .375 that it is difficult to argue that it falls in a different category. After all, it is not by chance that the 9.3x62 - and even more, the less distributed 9.3x64 - was to German Africa, what the .375 H&H was to British Africa. Another option would be a .300.
The bullet weight gap ranges between 7.8 g (120 gr) and 16.2 g (250 g). The 8x68S fills this gap perfectly from 9 g (139 gr) to 16.2 g (250 gr). Conversely, the .338 only addresses a small portion of the gap at the top end, from 13 g (200 gr) to 16.2 g (250 gr), and it is not far from duplicative of the .375. And again, the 9.3, ranging from 11.9 g (183 gr) to 19 g (293 gr) is so close to the .375 that it is even more duplicative, while not quite matching the .375 ballistics. There too, a .300 would work, with bullets from 8.4 g (130 gr) to 14.2 g (220 gr).
Versatility...
The 8x68S is a lot more versatile, and in a pinch can fulfill with the right bullets both the .25 and the .375 roles. If you only have one suppressed rifle, you will never be outgunned with it, neither in long range on small and medium PG, nor in killing power on heavy PG. The .338 nudges the answer, but it is really too much gun for small and medium PG and its trajectory is arcing compared to that of the 8x68S. As to the 9.3x62, it is anything but a PG rifle, and its trajectory is a true handicap out to 300 m. And of course, a .300 would also be a great solution.
Admittedly 8x68S commercial loads fall slightly short of the Namibia minimum energy requirement for DG (5,400 Joule), with the RWS 13 g (200 gr) developing "only" 5,200 J, and I do not know how strict or flexible the enforcement of the limit is, but reloading with heavier bullets (e.g. North Fork 220 gr, Woodleigh 250 gr) will get you to the legal minimum. In any case, whether at 5,200 or 5,400 J, I personally would feel completely OK using a 8x68S on Buffalo or Lion, and I have zero doubt that a solid will punch through an elephant skull from any angle.
So, should you ever need it, the 8x68S will do it all, better than the .338 Win, and better than a .300 that could not address the DG end of the spectrum.
Availability...
As long as Namibia is Namibia, there will be metric calibers ammo, and the 8x68S has been here to stay since the 1930's, and will continue to be loaded as long as Germans hunt. It is truly a GREAT caliber.
Parting thought...
In a perfect metric world, an ideal trio would be 6.5x68S, 8x68S, 9.3x64. I once could have bought a Mauser 66 with these 3 barrels. I could not afford it then, but to this day regret it..........................
And you could complete the 4 rifle battery with a 12.7x70 Schuler (dubbed .500 Jeffery by Perfid Albion) and be ready for anything
