I've never heard that they are daylight sensitive. The one thing I would do is put the greenhouse (I'm assuming this is a portable) over the spot where I plan to put the tomatoes so that the soil has plenty of time to warm up before putting those tender roots into the ground.

Would it be worth putting one or two in as an experiment? I would be very interested to hear your results. If you have any heirloom seeds, they might be your best bet. I've had heirlooms seed themselves in with no help or coddling from me. They might consider the assistance of the greenhouse as a vacation in Florida. Carmellia

The big thing with tomatoes is warmth - not so much light. I've tried all sorts of things over the years and one thing is pretty constant - only if you can get the soil warm and keep it that way will you get any "hurrying" of them. You can start them really early outside, they'll grow to a certain size and "stall-out" doing nothing until the soil temps and everything are perfect. If you put some in the ground in April and some in the ground at the start of June all the plants will STILL produce within a week or so of each other if they are the same variety. Your greenhouse idea may speed up their starting, but won't likely speed up when they will ripen as once you take it off the top the soil temp is going to regulate with soil around it. They'll just sit there most of May not doing much (unless we get a VERY hot spring) I plant mine out in Earth Boxes on Mother's Day as starts from my indoor greenhouse (I start those in mid-March) and I do get toms earlier than many folks, but that's because they are in boxes not in the ground.

Hope that helps!

-marie