You are right to go very shallow, those type of seeds need to be about 1/8 inch deep. I sew them then gently rake the soil around, then I have a weighted roller that I use to compact the soil. It works pretty well but the raised beds held the water more than an open field would, plus the raised beds had a lot loser composted soil. (the roller is actually made for installing glue down floors weighs about 30lbs)
The lettuce border would not have been bad but it came in too thick for it to grow well and in the middle there were 6 or 8 plants. I ended up putting several tomatoes in the middle so it worked out. It's one of the great things about gardening learning to improvise.