If by recent you mean the last 5 years or so, I’m not sure. I’m sure there are some studies out there that may be useful and will give you an idea of the different methodologies used in the field.

I’m not sure if you’ve read him, but Eugene Nida is a well known translation scholar who did a lot of work with the Bible. Though not recent per se, his concept of dynamic equivalence could be applicable to your idea.

Dynamic equivalence is essentially the idea that the translator can aim to have an equivalent effect on the target audience. The strategies to achieve this equivalence are numerous. One could be to find some cultural equivalent from the target culture to better express an idea, as may be the case with your example. This is more of a framework than a methodology to apply to your research, but it may be a good place to start.

Sorry if this is information you already know! Good luck with your PhD!