Thanks JJMR794,
I didn't know about the wire having a zinc coating. I think that is probably the culprit then. I will have to try wearing gloves until I can figure out how to finish the edges of the cages.
Here's the Illinois department of health page from which I got the info on bird mites:
http://www.idph.state.il.us/envhealth/pcmites.htm
"Rodent and bird mites may bite people when their hosts die or abandon their nests."
This led to the theory that if the eggs came from an infested hatchery, there might be hungry mites crawling around in the packaging or on the eggs.
"Mites that normally infest birds also bite people. The northern fowl mite (Ornithonyssus sylviarum) and chicken mite (Dermanyssus gallinae) primarily infest chickens, but also pigeons, starlings and sparrows. The northern fowl mite cannot survive for more than a month off its host, while the chicken mite hides in cracks and crevices near bird nests during the day and feeds by night. Cheyletiella mites infest both birds and mammals. They may prey on other mites and insects living on the hosts skin. They can cause a mange-like condition in pets, and itching in people who handle infested pets. They do not stay long on humans."
So, according to this, humans can potentially be bitten by avian mites...it just won't result in a highly contagious situation as with scabies.
Few things disturb me more than human parasites. Thanks everyone for helping me rule this out. Now I just have to find a treatment for my human bot fly larvae (kidding).
The main thing is knowing that,
if I were getting bird mites, I would be able to see them. For anyone interested in learning more about fowl mites (including size and photos), this is a good page:
http://chat.allotment.org.uk/index.php?topic=5250.0
Jennifer