But why is it that I feel uncertain about which premises I should accept?

Think of it as a foundational struggle: you've got non-rigorous ideas about what is morally true/right, and you are searching of a way to build a foundation such that any right idea will follow from that foundation deductively. Arguably, this task is impossible within human mind. A better human-level approach would be structural, where you recognize certain (premise) patterns in reliable moral ideas, and learn heuristics that allow to conclude other patterns wherever you find the premise patterns. This constitutes ordinary moral progress, when fixed in culture.