I have heard that Marigolds work.
Those 'orrible LWF's you refer to seem to be brassica specific, I have suffered them also in the past, they and their white detritus seem to adhere to leaves like glue.
Carrot fly are the cheekie chappies that you never seem to see as a fly, just as a wriggly thing eating the heart out of your carrots, before they fly off and start their life cycle over again.
An old organic deterent was proper old creosote, on a rag or two near the carrots.
Not the stuff available from B&Q, which I believe was introduced to stop creatures like bats being killed.
Real Creosote can be broken down by soil organisms, and so is considered by right thinking people to be organic.
Not widely available to anyone without a CPH number, but available online and at your local farm supplier.