How to treat severe cat fleas when her neck is scabby and irritated?

I am sorry to hear of the flea issues you are experiencing. That is certainly an unusual response to Capstar and it would be worth reporting this to the veterinarian that you purchased it from. You are right not to put the advantage onto the scabby skin, it could worsen the irritation.
A safe way of helping to remove some of the fleas is to give your kitty a bath with blue dawn dishwashing detergent. Whilst it has no protective effects it is safe and gentle to use.
Capstar is only one effective for about 24 hours so it may actually have worked, it just isn't helping longer term.
Environmental treatment for fleas is always very important too. Wash all of your cat's bedding and any blankets etc that she likes to sleep on. Your own bedding too if she is frequently on your bed. Consider steam cleaning all carpets and rugs in the house, and any fabric furniture too (like couches and chairs). You may need to resort to a 'flea bomb' product or call an exterminator if the problem is not easily controlled.
You can also look on your cat's body to see if there is an area of skin that is NOT scabby, where you could maybe apply the advantage instead. The back of the neck is preferred since the cat cannot lick it off, but you can certainly apply it elsewhere if needed.