"Neither slavery nor involuntary servitude, except as a punishment for crime whereof the party shall have been duly convicted, shall exist within the United States, or any place subject to their jurisdiction. "
Unfortunately I think you're right, the way the thirteenth amendment is written might make laws like this unconstitutional. What we really need is another amendment banning it entirely.
I've been pretty happy with Kagi and they have a decent privacy policy: https://kagi.com/privacy