Be wary of what is meant by objective and subjective. Subjectivity is neccessarily involved, because it is a domain of concern about persons, with their points of view. But science begins with investigations by persons, but uses tools like repetition, consilience, etc to achieve repeatable results based on abstractions tested as representing the system or process well. In ethics, there might be a transcendental subjective, that is the picture of the supreme deity in Hinduism, & of Leibniz's monadology, which allows universal statements about subjective experiences. I would also point to the role of mirror neurobs and intersubjectivity, as essential precursors to the layer of thinking ethics is in. And the insight from the Dunbar number to note our minds developed primarily to deal with oyr social landscape, rather than for tool use. It is complex language in particular, which facilitates us being able to be ethical rather than instinctive, the communion of minds in modes of life, another meshing of subjectivities. Rawl's theory of justice is I would argue based on this kind of intuitive intersubjectivity.
You should consider moral realism stances, rather than be looking fir objectivity in morality. Sam Harris in The Moral Landscape proposes a mathematical science of morality based on axioms, and I was arguing here that isn't tenable. A science of morality holds more water, but I was argue here that culture, especially religious and political culture, need to be thought of as part of a combined practical craft for building social cohesion and balancing people's competing concerns, which builds on what is already present culturally. In particular, I'd mention Durkheim's idea that holding shared values as sacred, binds together moral communities.
I have a particular interest in non-human minds, artificial general intelligences, animal cognition, and considerations around communication with aliens. I am surprised how few philosophers seem to directly consider these issues. Peter Singer has done a lot from his utilitarian perspective around ethics in relation to animals, writing Animal Rights which popularised that term, and writing The Expanding Circle which argues for a definition of moral progress which is expanding - and he has done work to support enhanced rights to be given legally to great apes and dolphins. Dinna Harraway in The Cyborg Manifesto rejects rigid boundaries between human, animal and machine. I asked a question about dynamic animal cultural intelligence in relation to our morality, but it seems it was deleted - I haven't found any philosophical thinking on this.
It is worth saying ethics do not have to lay claim to be universalisable, like Kant argued with the categorical imperative. Ethics can be pictured as a kind of therapy, a set of tools for a personal journey, analogous to a theodicy. I'd point to Stoicism as a clear example of this, especially Aurelius' Meditations, where an unjust and unfair world is taken as a given, abd the work is about what we can do with our own expectations, reactions and behaviours. This is very comparable to Buddhist ethics also. This is significant in relation to the charge of anthropocentrism, because animals or any other beings can readily be considered in their own terms - and Buddhism does so, considering not only animals but deva deities and hell-beings as moral persons we should have concern for and seek to help.
