Biodegradables. It reminds me of a little gift I received from someone, a cute little wooden box (4"x4"x4") with a sunflower seed in it and some peat. It says, start the seed in the peat in the box, then plant the box with the seedling directly into the garden soil later, and the natural wood would rot and become fertilizer for the plant, no kidding! When? You wonder who would produce such a brilliant product that makes zero sense, and for my husband to buy it?
Then there are some ideas that may work. For carrots, because of the deep tap roots, seedlings should not be too large before transplanting, and roots are not to be disturbed. To achieve that, sow 4-8 seeds in even distance from each other, per pot( 3x6"). Rather than separating each seedling to transplant, just dump the whole container out and plant the whole block in the soil. Thin out some as baby carrots to make room for bigger fellows to grow.
How about sowing seeds into paper tubes, filled with starter mix?