I finished the project. Thanks to everyone for the suggestions!
I ended up using the OCLC Fast API (fast.oclc.org/searchfast/fastsuggest) rather than saving everything locally. Tracking down the entire LCSH authority listing and parsing it into a simple data format was just unwieldy.
The search box I built suggests the LCSH terms from OCLC as well as LibGuides and LibraryH3lp FAQ links. jQuery UI Autocomplete is used for the suggestion functionality. The search box send actual searches to EBSCO Discovery Service. You can see it below on our homepage: