I've seen a lot of .338 and larger caliber bullets punch right through like you're describing. Unfortunately, none of your pictures loaded for me, so I'm not sure if I'm missing any vital info from them.
I will say that the reason I think this happens is actually too much mass in the bullet. A 300gr .338" bullet has a sectional density of .375 and to give you a perspective, a 250gr .308" bullet is about the same, and you'd have to go up to a 185gr 6.5mm bullet to get similar mass.
All that mass in that projectile is going to need a lot of opposing force in order for it to expand quickly and produce hydraulic force into the animal and inflict sufficient wounding for a quick and clean kill. That means a lot of resistance upon impact. So shoulder shots would be ideal, and you might have seen better results if you did fire into the shoulder. Shoulder shots also devastate the CNS and typically allow the animal to drop and bleed out or succumb to asphyxiation before it can recover.
I have seen these bullets expand better at longer distances (when impact velocity actually lowers) and I believe that's due to the delay in expansion overall, and impacting at a higher velocity causes them to exit before they expanding enough to produce hydraulic force, whereas if you slow that down they can expand before exiting. More resistance would help as well. Ultimately, it boils down to too much momentum at high impact velocities for that particular bullet and not enough opposing forces to combat they properly.
You could also step down to a 250gr or lighter bullet of similar construction and see better results too due to the decrease in mass, which decreases momentum, etc.
I personally have found using 30cals with heavy for caliber bullets (208gr-245gr) of softer construction balance out very well regarding penetration vs expansion, and work extremely well both close and far. I've gotten away from using larger calibers because the results just tend to not be worth messing with it. Of course the same principle work with smaller calibers as well, but there are other factors and considerations that need to be taken into account going that route too.
Your examples that you say have worked well are actually good examples of bullet size and construction that do indeed balance well.