In moving towards unschooling, I think it helps to *add* things rather than "eliminate" things. Adding is more likely to be positive - more flexible and open-ended. "Eliminating" is not many steps away from a rule, from rigidity. Yes chores / No chores. Both are rules - rules which intrude, regardless of what's really important.
What is important for your family - peace? joy? doing fun things? well-being? growing and learning? comfort? delight?...
What can you do to enhance what's important - more flexibility? more listening? more engagement? more calm? more kindness? more fun ideas? more soft places? more interesting/happy options? more generosity? more creativity?...
From the outside, unschooling may look like no chores, no bedtimes, no education, no discipline, no structure, no limits, etc. But from the inside, it's about learning, relationships, living with real parameters, partnership, navigating turbulence, making connections, joy, curiosity, focus, enthusiasm, options, following trails, fun, growing understanding, opening doors...
"Eliminating chores" won't, of itself, bring unschooling closer. The conditions which led to and continued the imposition of 'chores', need to change. And that takes time and deschooling. Many steps in the direction of understanding about learning, of awareness of control in relationships, of relationship-building. "Eliminating chores" can be done with a few words. Getting to unschooling takes more - it requires parents to change significantly. Step by step is usually more effective than trying to leap across. More tortoise, less hare. :)