Once they sprout you need to get them off the heat and under lights. Of your selection, peppers will take the longest to germinate, next the toms. Cucurbits sprout quickly and grow fast which is why most growers wait until their soil is warm and direct sow them.
This is the problem with mixing varieties under the dome. I would carefully pot up your cucurbits to individual pots or cups. That way you could keep the heat and the dome on for the others. If you still have seed for your cucurbits you'll have back up to direct sow if you can't pot up or things don't go well.

an update and a thank you. got the other lights set up and got the sprouted guys out of the dome. things look to be moving along nicely. I'll plant these when they are ready and direct seed some of the same variety. I am curious to see if I get early harvest or the direct seeds catch up anyway....

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