To all who followed and helped with this post:
I FINALLY figured out why the fresh eggs were stinking!
Our temps started getting back up into the 100's again and the egg smell came back!
But this time, I noticed what was happening.
Firstly, a hen broke an egg in the nest one morning. I cleaned it up, scrapped the wood beneath the nesting box as best as I could (I use the bread crates, the ones bread delivery trucks use to transport the loafs of bread in, filled with hay), then put fresh hay in and replaced the nest. However, I didn't get all of the broken egg up because the rotten egg smell was back by evening.
Also, by that evening and the following day, the fresh eggs where smelling bad. So I removed the nest completely and rescrubbed the wooden bottom of the nesting area. I left the nesting crate out for several days before replacing it.
Problem solved!
Apparently, since egg shells are porous, the excessive heat combined with the body heat of the hens sitting on the eggs allowed the rotten egg smell from the remains of the broken eggs to permeate through to the fresh eggs. So, when I first started having this problem, I hadn't noticed that an egg had been broken in the nest because there was no evidence by the time I noticed the smell. And even though I had cleaned the nest as a precaution, I hadn't cleaned the wood below the nest as thoroughly.
Therefore, I'm happy to report that my hens do not have some sort of strange infection or disease! YAY!