Interestingly, you would actually LOSE resolution by using the D300s over the D810! Because the density of pixels on the D810 is greater than on the D300s, in fact you get more "crop factor" by simply cropping into the D810 image than by using the d300s which is only a 12MP sensor. In fact the D810 is a 15.3MP camera in DX mode!
For direct comparison of the two sensors, click here:
https://www.digicamdb.com/compare/nikon_d300s-vs-nikon_d810/ As for the main question what to take to Alaska, have you heard the phrase "brown dot, white dot"? Aka bears, Dall's sheep and bald eagles when photographed...especially the sheep! First of all, you have already have a kit that we could only dream of a few years ago. The D810/200-500 is a killer combo and will serve you very well!!! That said, my own experience up there is that your lens can never be too long!
Two ways to add more reach to your kit: Teleconverter, or your original idea of a high resolution DX body.
Per Photography Life, a TC does work well on the 200-500:
"Nikon TC-14E III (280-700mm): When testing the 80-400mm lens, I personally did not like how the lens performed with the 1.4x teleconverter – AF speed and accuracy suffered a lot. Before I slapped the TC-14E III on the 200-500mm, I wondered if I would get similar results. To my surprise, the Nikon 200-500mm actually did quite well! While both AF speed and accuracy took a little hit, the lens did not seem to suffer as bad as the 80-400mm + 1.4x TC combo. In daylight environment, the lens performed really well, making it a nice 280-700mm f/8 combo. It is important to point out that I was shooting with the Nikon D750 and D810 DSLRs, which have excellent AF systems that can focus with f/8 lenses using the center focus point (if one were to use an entry-level or an older generation Nikon DSLR, the results would not have been as good)."
Birds in flight? Probably not, but the aforementioned sheep dont move fast! And where I really would want it is shooting from the ship as you glide past the otters with pups on their bellies!!! Again, speed of focus not so critical.
The other route is rent a D500/D7500/D7200 and put more pxels on the target like you were thinking with the D300's. 20-24MP-DX does give more reach than the D810.
Finally, take a really good pair of binoculars! Best not to see the whole trip through a viewfinder! And have fun! Its a wonderful adventure!
Dave