It is a membrane, but not a mucous membrane...
What you are doing GH is likely way more than enough. Boiling it once should be plenty, if you are concerned about bacterial.
Mine go straight from being used, unwashed, into my kitchen compost bucket, where they stay about a week. Then they are dumped in the compost pile, where they stay a few months. Then when I use the compost, the eggshells aren't broken down (though they may have gotten crunched up a bit), so I pull a few of them out and put them where they are most needed, like brassicas and tomatoes. Some I just crunch up a little more and leave in the compost, to enhance the general soil.
I figure a few months of sitting in the compost pile, being rained on and acted on by all the forces in the pile cleans them as well as anything else I could do... Don't fuss, let nature do it!
That's my mantra.