I think the conclusion I have come to is that, as a newly constructed name, it's pronounced however you want it to be pronounced. You could say I'm responsible for the name's creation, being the one to put the letters together in English for the first time, but it wouldn't be very meaningful for me to try to be like "It's objectively pronounced Ro↑ze ↓myne↑ and anyone who pronounces it otherwise is wrong." Likewise, it's not very meaningful to look to the Japanese, because Japanese names are almost universally pronounced differently from English names, and, for example, you wouldn't really learn much about how to pronounce Lutz or Gunther by looking at Ruttsu or Gyunta. Rozemyne is no different. The anime dub for Season 3 will no doubt have to dub Rozemyne (though of course they will have it written as Rosemain, or Rozemain at best). However, in that case it will be the dub director arbitrarily making a decision. There's no transcendental correctness or truth to the pronunciation that will be given by that - he is, just like me, just another dude.
In which case, I think only one conclusion can be made: There is no pronunciation for Rozemyne beyond what you think it is. It's a made-up name and English has inconsistent pronunciation rules for letters. The author can't give this psuedo-English name an objectively correct pronunciation, I can't give it an objectively correct pronunciation, and the dub director can't give it an objectively correct pronunciation.
A conclusion for Rozemyne's pronunciation can only possibly form through time and trends - through decades of people reading Rozemyne, pronouncing Rozemyne, and so on. I imagine that, much like names IRL, there will be different regions where some people pronounce it one way and other regions where some people pronounce it another way (much like the infamous "New York Mario"), but that's just how it goes. This will be a conclusion founded in oral history, rather than me arbitrarily deciding it must be pronounced one way, or anything arbitrary like that. Of course, I imagine the dub director's decision will have HUGE influence, as people mimic what they hear, but it only become meaningful through the following decades of use, rather than the decision itself.
tl;dr Ask me again in 30 years