So in case anybody cares, what happened was that I apparently have a theme that got hacked. It appears to be a theme called super blogger had a helper.php file in it's images directory which allowed files to be posted into that directory.
Using that uploaded file, extra code was added to my functions.php file in my standard theme which opened a backdoor and gave free reign.
Many thanks to Alex McKee who helped me track things down.
I recommend reading this post from Dave Meehan for more detail.
FYI, a couple things that should have clued me in (which I'll look for in the future). First, I started getting an error on my admin console about extra data sent before the headers. I stupidly went into functions.php and fixed it (even working with 8Bit support) without noticing the added code. Second, in the source to my pages, there was a misspelled "Wordpres Counter." That should have clued me in as well.