From my experience, over-feeding is a sure way to get a gnat infestation (too much food = gnat infestation).
Remove the food in the worm bin until the gnat infestation is under control and coverup any remnants of food with castings, compost or bedding. The BTI take care of the larva over time. Spinosad will poison/kill the microbes that your worms are feeding on... You don't need it. Use a sprinkle of diatomaceous earth (DE) over the content of the bin. DE is sharp and causes cuts and serious wounds on the adult gnats. DE is effective when dry but not when wet and DE won't cause harm to your worms. DE consists largely of silca.
After the gnat infestation is under control start feeding the worms slowly, hiding the food under/inside castings, compost or bedding and look for the correct balance of bedding, compost, castings and food.
The most important thing that I did to improve the balance in my worm bin was to add homemade compost. The worms feed on the compost, sleep in the compost and gnats aren't attracted to the compost.