I 've been looking for information about this topic, but as mentioned above, there is not very much to find on the internet. The only thing I would like to point out that is that 'Rhyndam' should be spelled Rijndam or Ryndam
USS Rijndam (ID-2505) - Wikipedia a ship in service for the Holland-America line.
As for his motivation or ambition to celebrate Mass on Titanic, I can only give my opinion.
I think that Mr Kotheimer, as a freshly ordained priest was in need for a parish. In those days, there were more priests than nowadays and all had a kind of assistant priests at their disposal in the parish. I bet it was tough for Mr K. to find a parish and so he tried his luck to be chaplain on an ocean liner. WSL wasn't perhaps very warm to have a RC priest in their service, refused and thus Mr Kotheimer cancelled his tickets and booked another ship.
If otherwise, Mr K. cancelled because he couldn't have a Private Mass during his journey to the States, then he must have had rather strong beliefs and having wanted to take the lead in the celebration of holy Mass solely by himself (I'm sure WSL would have pointed out that some colleagues would be taken care of it during the voyage). I can hardly imagine him wanting to cancel and rebook tickets he already purchased for this reason only, knowing his mother and sister would be travelling with him as well. But again: those are my opinions, I'm trying to analyse.
What concerns the rituals of wanting to say the Mass, it is rather complicated, as mentioned above, until the 1960's it was a tridentine mass
Tridentine Mass - Wikipedia, whole in Latin, the priest not facing the crowd, a lot of praying, standing up from the benches and sitting down every 10 minutes or so. Furthermore the priest needed a lot of communion bread (1pp) and some wine (only for him) to perform some rituals, and I don't know if Mr. K. would have taken care of those logistic issues.
Anyway, it would be nice to know if he got what he was looking for on the Rijndam (He got some parishes after all). And I find him very lucky to not have boarded the Titanic. I think he was too. It 's a nice colourful history. I hope to hear more of it.