I myself would much prefer to start at .40 & up on a dry land Hippo to be certain I was the one that killed my Hippo .
On land & up close you might not have time to pick the Brain shot properly & body shots just don't stop Big Hippo Bulls well with the .375 (none really will but bigger the better) you might have the PH shooting him & or he will make it to the water, that's not a deal breaker but much more work for all, if he makes it to you then that is far my work, either for the Hospital or Mortuary staff !
I would at least use a Premium expanding bullet for my first shot, The 350gr bullet doesn't seem to greatly up lift the .375 H&H performance either, after using them & seeing them used, doesn't make them into .416s as you would dream !
While the Cup Nose & Flat point Solids have a much greater kill effect, just be sure (Check this in you rifle) that they will feed as more than a few factory rifles will not feed them (actually have trouble feeding anything well in the field) !