I just had six day germination with heliotrope seeds -- marine variety. It stunned me!
I bought them from a good online seed supplier. I planted them 1/8" deep in regular compost, in a plastic container with a plastic lid, with drainage holes punched on the bottom (from the supermarket, nothing fancy). Put them on a heat mat which has one temperature setting, under a cheap seedling starter light.
Yesterday, there were 25 heliotrope! I did not expect much success, and I also thought they would be a month or two before growing. Good thing they overwinter pretty well outside where I live, most years!
I took the lid off, they flopped over, so I propped it up with a pencil and today, a book, and I'm taking them off of the heat when they are a little bigger because they are tiny.
But these were super easy to propagate, and I do think it was the heat mat and light that helped, along with constant humidity. The seedlings are TINY, almost like foxgloves.