Alright Greg, I'm posting a link to the 64-bit version of libxml2.so that was in use on the very system that I created every single one of those "unofficial" Sigil binary packages with (v2.7.8).
If you're game (and after you've used KevinH's advice to verify you HAVE the issue), then just rename the file without the "_x64" (so it's just named libxml2.so.2) and place it in your /usr/local/share/sigil directory.
If you need help with the specifics of achieving that, I'm hoping some kind soul will be able to assist you -- not that I'm not kind ... I'm just a horrible instructor. A man's got to know his limitations.
It's on my google drive.
https://drive.google.com/file/d/0Bwu...ew?usp=sharing