This paper investigates how gender-fair strategies in source texts influence the production of non-binary translations in the Italian to German combination. We make use of a controlled test set featuring both binary and non-binary approaches to assess their effectiveness for non-binary renderings in the target language. We also introduce an automatic evaluation framework that classifies target sentences into four categories: non-binary, binary-gendered, single-gendered, and incoherent. Relying on human annotation and analysis, we compare Reasoning LLMs against standard inference, examining whether reasoning improves translation quality and automatic evaluation. Our results show that reasoning models are more successful in shifting from binary to non-binary formulations and in handling linguistic challenges such as epicene terms and special characters, although there are no improvements in sentence-level consistency and evaluation accuracy. A qualitative analysis of German translations shows that reasoning encourages the reformulation of source-side strategies through neutralization, visibility strategies, and paraphrasing, resulting in more natural target texts.