Firstly some photos to show the size of what I'm dealing with

[img]https://i164.photobucket.com/albums/u3/berru_photos/2011-09-19111049.jpg[/img]
These are the biggest tomato seedlings. I'm pretty sure I'll just plant them out at this stage.
[img]https://i164.photobucket.com/albums/u3/berru_photos/2011-09-19111107.jpg[/img]
Watermelon, smaller toms and rockmelon
[img]https://i164.photobucket.com/albums/u3/berru_photos/2011-09-19111125.jpg[/img]
Capsicum...these buggers are taking forever.
[img]https://i164.photobucket.com/albums/u3/berru_photos/2011-09-19111147.jpg[/img]
Cukes and smallest toms.
[img]https://i164.photobucket.com/albums/u3/berru_photos/2011-09-19111155.jpg[/img]
Basil and coriander.
[img]https://i164.photobucket.com/albums/u3/berru_photos/2011-09-19111840.jpg[/img]
Strawberries and mint...next time I'm buying seedlings

Okay, so my ideas. The only one I'm vaguely sure of is potting everything up (because that'll mean they stay moist a bit longer, right?) The cukes and melons will be grown in containers this year anyway, so a bit early shouldn't hurt them?
What about moving them all into shady areas/areas where they get dappled sunlight/only for a few hours a day?
Just how bad would putting the pots in trayfuls of water be? Or would this be okay for some of them and not for others?

Sooo, are any of these worth giving a try, or do you guys have any better suggestions?