shade Think I can take my plants outside under a shade cloth?

My seedlings are 4-8" tall. Annums (jalapeño, poblano, cayenne, cascabel, shishito) on the taller side, chinense (scotch bonnet, choco bhutlah, red Moruga, yellow BBG7, Bahamian goat, etc.,) on the shorter side. Germinated from seed in early March, been under T5 for 17 hrs per day since. Still in solo cups.

I've taken them out periodically (mostly on the weekends) to get some real sun and they have responded REALLY well. They have gotten as much as 1.5 hrs between 10-2 and 3+ going out at 2 through sundown. Some nights in NorCal this time of year might get to low 40s but it's rare. Daytime temps 65-75 with days warming up and the occasional 85 or so.

Would they cook if I move them into 5 gal pots (I'm afraid they would dry out in solo cups) and put them under a 30% shade cloth all day? Would a thicker cloth be better? I would prefer to not buy multiple shade cloths but could if needed.

I don't really get home early enough from work for them to get good strong sun. I don't want to kill them but I'm antsy to get them outside where I think they will really take off.

Thoughts?

Mine are outside in the northbay and prolly a scoche smaller than yours and are in 4" pots, no shade cloth. Not knowing how hardened they are I would do it on the weekend so you can watch them. They should prolly be fine under the 30% shade cloth though. But safe is always better than sorry, do it on the weekend IMO.

I personally just put my plants along the northern wall of my house.  There is an fence on once side, and a bush on the other.  Very little direct sun hits them.    I then move them into filtered sun for 4-5 hours a day, and finally into the garden in 7.5 hours of full sun.   
 
I think once a plant recognizes how bright the sun really is they harden off pretty quickly.  
 
Although i have had some temperamental peppers recently.   Being a drama queen in the sunlight. 

If you're in a fully exposed spot - that is, open, no shadow, then 50% shade cloth full time for at least a week. After that, good to go... I would put them in their final container, at this point, but that's just me.

Awesome thanks dudes! I'm ready to go for it.