Medic within Her Imperial Majesty's Star Navy

Technically, this is a question about grammar. However, I put it here because it pertains to the Skaran Empire. Which translation below fits the job description "medic within Her Imperial Majesty's Star Navy" better?

Genitive: Medika Klassis Stélláris Augustai (reverted ae diphthong to ai), or
Ablative: Medika Klassí Stéllárí Augustá
 
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