I don't understand that you have said you use raised beds but also grow in the soil in your yard? Perhaps you mean you have delineated some sections for growing but are still growing in the soil itself. Can you add other soil to the raised bed and grow in that? (Example: your raised bed is 6" high so you add 4" of your preferred soil mix to the bed, and grow in that)
If not, then just keep composting and adding in to the soil. It can take years but you can surely convert the soil. If you don't have as much materials for a compost pile, you can still achieve some success by using trench composting whenever you do have some small bag's worth of fruit or veggie scraps.
Some plants that should do well in that soil are
1) aloe vera (might have to bring it in for the winter)
2) green onions
3) rosemary
4) purslane
5) salvias
6) canna lilies (it is also edible although many grow it for the flowers)
