Tiny seeds for carrot, lettuce and thyme can wash away if they are planted in the ground. My solution has usually been to plant in flats or pots.
Have you used seed tape and disks? Would you use them again?
On the other hand, I have made my own seed tape type of planting thing with single sheet paper towel or bathroom tissue or even a single sheet of Kleenex tissue. You can use honey or cornstarch water to mix with the seed in a squirt bottle.
Here are some DIY instructions for making your own.
My other tried and true method for starting fine seed: plant it on damp potting soil, cover it with damp, cheap paper towel (thinnest is best) and mist it daily. The seedlings pop through the damp towel quite readily.