1) Carrots are transplantable. If you start them in a flat, when they are about 1-2" tall, you can tease them out of the soil with a toothpick and transplant them to where you want them. As soon as you have the first set of true leaves (something to hold onto), you can move them, but don't wait too long.
2) Mix the carrot seed with some soil and spread it as a thin layer (1/4" or so) over the wood chips. Mixed with some potting soil, the seeds shouldn't be washed too low into the wood chip layer to germinate.
3) Another version of the last one is to lay down a row of topsoil on your mulch, say a few inches wide and a half inch deep. Make your furrow into this ribbon and plant your carrot seed as normal.