Your plants look amazing! Great job. What is your unheated greenhouse like? A reasonable sized one with automatic vents and such? Bob Flowerdew recommends putting in lots of black painted jerry cans of water to help retain the heat over night. And our neighbor has her tomatoes outside in the ground three or four weeks before me as she has these red sort of water sacks composed of tubes of water she fills to help retain night temperatures. These sorts of things only get your tomatoes out of your house a few weeks earlier than normal. And don't rush the hardening off process, especially with them being larger - more leaf surface area to toughen. Also, I recommend you putting a gentle fan blowing on them one a day from various directions each day.. so they don't get thrashed on their first breezy day outside. Unless you plan on planting them in the greenhouse?
Blue onion its only a tiny 5 shelf plastic job, nothing fancy (no room for anything larger unfortunately). I may have a go with the fan as you suggest; they're very pampered plants!
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Also, I recommend you putting a gentle fan blowing on them one a day from various directions each day.. so they don't get thrashed on their first breezy day outside. Unless you plan on planting them in the greenhouse?