I'm not sure why it took me so long to realize I could do this, but this week I was able to figure out how to add a page to my website to make available signed copies of my books. I was even able to put in a field for people to request special dedications. You can see them here.
This all happens with a slight amount of hassle. After all, I will have to select the book, sign it, and take it down to the post office to mail. Since the copies are a bit more expensive than the Amazon price, however, (to cover shipping and packaging charges) I don't expect to be overwhelmed by requests.
In fact, no one has yet ordered one.
So if you read this post, decide this is absolutely something you would like to have, try to order and have any problems, then please email me at firstname.lastname@example.org and let me know so I can fix it!