Here are some suggestions I have for your little babies.
1. You said you often had die off upon hardening off, you might want to try going real slow. I harden off by putting out plants for 1 hr in the evening after work, then 2 hours the next day, 3 hours the day after that, then 4 hours in the evening for about a week, then during the work day for another week in shade, before a few days in full sun prior to being put in the ground.
Granted, I am in a much cooler area than you are, and the hardening process can take a whole month as the plants don't do much growth while hardening outside and freezing temps can delay planting out. During hardening times, if temps are below 34, tomato starts only get to harden for 2 hours before bringing them back in too, so that can prolong the process. If it's the 35-45 range, they are out full time as planned.
2. It looks like your plants are really leggy. I would try and give them more lighting with your grow lights in addition to the window. When I do zucchinis, their first few leaves around the cotyledons are probably 2-3 inches long from center to leaf tip and sit squat in the pot.