Not quite sure what you mean about the buckets. Are these inverted over the top of the plants?

no, the seedlings are set inside. this method has worked well for me after they've had proper light exposure

I had to plant 3 melon seedling in my garden without hardening-off but used a rather thick agro-cloth over them as protection. It seems to be working but there has been very little sun since I planted them so that could be part of my success. Hopefully the weather will remain cloudy and cool for a couple more days so they can settle in before the sun comes out...

"Temps in sun are mid to high 50's only."

If it is still that cool it may well be too early to harden off many things. Plus you'd have to bring them back inside at night which kind of defeats the process of hardening-off. What crops are we talking about specifically?

Dave