These all seem to be such good ideas for better success. Even the one for sowing the winter before - that
might work here where we have sub-zero winters, I'm not sure.
I'm going to do more than say these are "such good ideas" and add a few things that have worked for me. (Unlike the
keeping track of what is going on under the board trick

.)
First, the easy one: buy
pelleted seed. A number of companies offer it, Johnny's, Harris, are 2. That clay coating really helps keep moisture against the seeds during the days it takes for them to germinate.
A little more difficult is somewhat like making seed tapes, which you can do, also. I just have quite a few feet of carrots I'm trying to sow - besides, the paper tapes kept blowing away before I could get soil on them

!
Anyway,
Fluid Seeding, or a variation on that. Fluid seeding is used in the west with alfalfa seed - another tiny seed sown shallow and subject to drying out. In the garden, I've used cornstarch gel as my "fluid" and just sown the seed in the gel.
One tablespoon cornstarch to each cup of water is brought to a boil on the stove. Allow it to cool a little, pour it in a suitable container (I fill a zip-lock quart bag at a time) and head out into the garden. Drizzle the gel in your furrow and sprinkle the carrot seed on top. You will use more gel than if you make seed tapes but cornstarch isn't very expensive.
This has worked just as well as pelleted seed for me

. I have used it for lettuce seed as well but lettuce germinates so quickly anyway that it isn't a very important help.
Steve