For the old relic you use a crafting weapon melded, it doesn't sound impossibile for an esoteric weapon to be the "base" of the new relic. While for the bonus it can be anything, maybe you need to infuse an empty materia with the soul of some monsters and bosses but instead of doing it you can infuse your zenith directly into it skipping the killing part. After all those who had the original 1.0 relic skipped all the craft/meld/primals as well.