Thyme is a dry land plant so the soil must be well drained. I have problems with thyme too. They like water but they like to be almost dry before watering again. Try planting outside. They like a loose soil with good drainage and slightly alkaline. In pots, I make a cactus mix which dries out faster. You can get cactus mix at Home Depot and other places. I do add a handful of peat to the cactus mix for seeds so it dries out a little slower. Bottom water is fine as long as you dump all the water out of the tray after about 10 minutes. Outside, I start my seeds in pots or trays in full sun and I water them daily. I have humidity around 80% and day temps around 80 degrees. When I grow thyme in pots in peat based mixes, they do ok for a while but they get woody. I also live where is rains a little almost every day. My mom grows thyme and sage and waters twice a day, but she lives where it is hotter and drier and I think she sprinkles more than waters.
Happy gardening in Hawaii. Gardens are where people grow.