First thought is you should start with cuttings, or transplants if you don't have friends who will give you cuttings. You gain months of growth time that way.
My only idea on the babies is that your potting mix looks quite coarse for seedlings. I always use a seed starting mix, that's much finer and would hold more moisture. Seedlings should never be let to dry out. No specific experience with coleus seedlings, they just seed themselves in my garden and I transplant them when they're an inch or two tall. But I start lots of other seeds.
Suggest you buy a little bag of it, put some in small pots and try to transplant a few of your seedlings into it. A tiny spoon works well for moving seedlings for me. Chop sticks are also handy for the little tiny plants if you can manipulate them, so you can be very gentle and not break the roots or stems. You need to thin those seedlings anyway, they can't grow much that close together.
