I agree that small containers should not be put on asphalt. I would actually shade them during this part of the year, when daytime temperatures are usually > 80 anyway. Put them on the north side of a small shrub, plant, or another pot to still let some sunlight get to the leaves. Patience is the key here. Don't take the cuttings out of those containers until you see lots of roots. No more humidity bins, etc. At this point the outdoor environment is mostly ideal for cuttings, as long as you keep the root zone shaded.
I had one very thick cutting that I had in sphagnum moss all winter and spring and it didn't do anything. Ends started to dry up. I actually forgot about it, then a few weeks ago, I said, oh crap, what's up with that cutting? Went down to the basement and there were a lot of roots and shoots. Stuck it in a 1 gallon pot, and shaded it as I describe above, and it is now taking off. But I won't be re-potting it until next spring most likely.
As long as the cutting is not rotten or dried out, there is still plenty of hope, even if you break some roots, and if leaves shrivel and die.