Stick with the raised beds or planters , last years tom compost with 30% sand or use just sieved garden soil .
You do not need a very large raised bed.
Sow the entire surface and it will come up solid carrots but with such density you need to keep on top of the watering.
I use Early Nantes and get tasty finger size carrots much nicer than the 'Horse carrots'.
I consider myself a reasonably good grower but never had real success planting in good ground with bare patches and complete no row shows.
The garden can then be used for stuff that wants to grow there .