Becky, bottom-watering should only help if the top 1-2 inches of soil at the top dries out. Not sure if you can let that happen to young seedlings without deep roots.
Check out this really
helpful article which states:
"The most important strategy to minimize fungus gnat problems associated with houseplants is to allow the growing medium to dry between watering, especially the top 1 to 2 inches. The dry-growing medium will decrease survival of any eggs laid and/or larvae that hatch from the eggs as well as reduce the attractiveness of the growing medium to egg-laying adult females."