Wow! What an adventure! Of course I went out there and tested everything. The results were quite interesting.
First of all, I found that I had a bunch of "users" and another "admin" in the Users area. WTF???? They went bye-bye, and I changed the password.
After reading about how the redirect could take place in the header.php file, I opened it up and it looked normal. HOWEVER, when I opened it up while in WP, it was filled with junk. First thing I did was replace the file with a pristine copy from my theme folder on my desktop.
Nothing. It still redirected. So I deleted everything in the header file while in the editor, and selected and copied everything from my pristine copy, then pasted it in the file.
Ta da! Cured.
A quick update to 2.9.2 and my problem is, apparently, solved. I think the key (at least in my case) was a classic "lessons learned." I made sure that my new password is ever so much stronger, and I think that i've got it locked. At least for now.