Identifying and Propagating a Mystery Succulent

I have a succulent growing on my lanai in Southwest Florida that I'm trying to identify and propagate. It gets late afternoon sun, needs very little water, and has more than tripled in size in under six months. The stem is becoming woody, and it has variegated, nearly heart-shaped leaves with serrated edges—bright green with a creamy border. When crushed, the leaves give off a minty herbal scent. Part of the plant has reverted to solid green, suggesting it might be a hybrid. It's getting leggy and cascading over the pot, and it produces spires of tiny, lavender flowers with no fragrance. It's planted in a plastic pot with drainage, using a mix of compost, potting soil, and heavy mulch.

I'm considering four propagation methods: (1) letting a cutting callous, then laying it on its side; (2) dipping a cutting in rooting hormone, letting it callous, then potting upright; (3) dipping in hormone and potting immediately; and (4) rooting a cutting in water. Which approach would you recommend?