I think your April 1st timing is good. I'd start the veggies that don't mind cool temps then and save the tomatoes and any other heat lovers for about April 15th.

You may want to use a simple light fixture with a 40 watt bulb to help keep the temperature up at night, or use heat mats specifically for seed starting. I'd put a thermometer inside so you can monitor the temperature. I don't think this type of greenhouse would retain much heat at night if the temps got down below 25 or so....maybe lining it with bubble wrap would help and having jugs of water in the bottom that would absorb the worth during the day and release it at night.

You may also want to post this on the greenhouse forum....there are some very knowledgable people over there who have tried all sorts of things. If it were me, I'd try it....you never know what might happen. If you lose anything early, you should still have time to start more later in April and not be behind once planting time comes around.

I just got this in my Farmer's Almanac e-mail today. Maybe it will help you gauge when to start each plant.

Here is a link that might be useful: Growing Vegetables