WAY too much epsom salt for any life stage is your biggest problem.
Young plants need very weak, if any, fertilizer. In MG soil there is already too much ferts for young seedlings, so they were starting off 'hot', then the addition of the liquid nute and epsom salt put them over the edge.
Combine that with being very close to a big lamp (too close unless it is air cooled correctly) and you are seeing the fert burn magnified.

Flush just using plain water at pH 6.7, raise the light (BTW, HPS is for flowering primarily, and you can get great results with CFLs in veg and they run cooler), go to a steady feeding of your liquid fert starting at 1/4 the recommended dosage and working up slowly.