David,
Your seedlings might be a little etiolated as they seem to be STRETCHING. They should lie flat to the ground. GRADUALLY introduce them to more light and they should start growing more normally and forming a rosette. Do keep the seedlings MOIST but not WET as they have tiny roots at this point and you can lose them, although your portable grow box will hold in the moisture better than a simple pot.
Your climate is perfect for semps and you should be able to grow them with no problem. A few might not like your winter wet but most will be good.
Kevin
