Okay, so there are like 600 problems in this photo. That's probably why you are having trouble.
First - it looks like you have a tray inside of another tray. This causes problems like 85 percent of the time. Usually with all the water running to the center.
Second - your light is way to close to your starts.
Third - It looks like your light is the only source of light. That's why things are so leggy. Get that setup next to a window if at all possible.
Fourth - the dryness - this is your main problem? There is a saying out there that goes something like "Be mindful of your corners and your edges and the centers will take care of themselves" This basically means water from the outside in.
Continuing on that dryness thing. If at all possible get something solid under your tray. The airflow is probably one of the reasons thing are drying.
I could keep on firing here - but those are some of the adjustments I would look at. Please update us as your plants continue to transpire. I'm sure we get your plants and you happier with the results.
Just minutes ago I raided the tray on the left and put my tomatoes in
bigger containers filled with a "special mixture". Now, if my mixture doesn't
kill them and they recover from transplant shock, I will start putting them outside
I would pinch those off at the soil.
Thoroughly moisten the soil and replant.
Cover with a tray top or clear plastic to keep the humidity up.
If you keep it covered, you probably wont need to water again until they sprout and you take the cover off.
Don't use the light until 3/4 of the tray has sprouted. Remove the plastic then too.
For extra help -
If you don't have a window to use for extra light, reflect light on the sides with tin foil walls made by covering cardboard with foil. A couple of mirrors would work too.
If you have a fan, you can use it on a low setting to blow at the plants and increase stalk strength.
I have had pretty much 100% success rate covering my seeds until they've germinated. I've done that in a variety of ways. Some of which you can look at my blog to see. Just put a trash bag around it until everything is germinated. That's what I'd do.
I agree that you don't have enough light but not that you have it too close. My setup uses two 48" 2-lamp fluorescents with one cool blue and one warm red bulb each. I have a seed starting tray like yours that has a bottom tray that holds excess water and a clear cover or humidity dome. I don't use Miracle-Gro or any other fertilized growing medium, only pure coconut coir. I cover the seeds until they sprout and use some form of bottom heat (top of refrigerator is cheap or heat mat for $25). The lights are placed within 1" of the seedlings and raised as the plants grow. You can't burn the plants with the fluorescent bulbs but I try not to let the plants touch the bulbs as they grow. I add water to the bottom tray if I'm feeling lazy - instead of watering every cell individually. If yours is pooling in the middle it may be warped. Once you have true leaves and some decent growth started you can add diluted fertilizer. I pot the seedlings into 3" peat pots after they are strong enough to be transplanted and continue under the lights until about 8 weeks or when the garden is ready. I finally put leggy seedlings behind me once I found this system. Just remember to harden off the plants before they go out into the sun.