Is the soil kept evenly moist, not soggy. The tops will dry out before the bottom and seeds are fussy, they do not like to be either soggy or dry out.
Try some seeds in a couple of 3 inch pots using the potting mix. Make sure the potting mix is thoroughly moistened but not dripping wet before you fill the pots. Water the pots thoroughly after the seeds are planted to get the air spaces out. You don't want dry spots in the pot. Put the pots inside a mini greenhouse. (a.k.a. large Grape container from Costco. They have holes in the top and sides, or make a humidity tent.) Fast germinating seeds like tomatoes, beans, lettuce should be up in a week. You may not have to water the pots inside the tray since it will dry slower, but check every couple of days to be sure the soil is still moist by feeling it or lifting it up to gauge its' wt. If you have to water, bottom water by putting the pots in a shallow tray with about 1/4-1/2 inch of water for about 15 minutes. Then put it back in the mini greenhouse.
If this works, then it is not the soil but the way you are watering that may be the problem.
I water everyday, but my seeds are started outside on a bench master so air circulates and the mix dries out daily. Indoors on a bench with no air circulation, pots will dry out slower. Bottom watering can be tricky. You need to make sure all the water is soaked up and the trays emptied and how to test when they need to be watered again.
Even outdoors, I prefer to plant seeds in shallow pots and trays rather than individual cells. I have way more problems since the cells seem to stay much too wet for me even though I am using the same mix. I think it is because cells don't have as many drain holes. I plant my seeds in community pots and transplant out to individual containers when they have true leaves. I even do this with the harder to transplant dill and beets. I will lose a few in the process but less than I will if I used individual cells. For plants that don't like too much water like dill and lavender I use tofu containers since they are wide and flat and the plastic is strong. I make holes in them with a soldering iron. I do have to use a mask burning plastic is toxic.
Happy gardening in Hawaii. Gardens are where people grow.