As it turns out, I had a lot of difficulty getting Spatialite to work. I was able to get the pod installed and everything seemed fine at first, but later I realized there was a problem with the compiled architectures; no 64 bit. I found a Homebrew example where all of the architectures were built, but the resulting file size concerned me. Ultimately, I dropped back and went with vanilla R*Tree because the fast indexing is my primary requirement. Some of those spatial functions written into Spatialite would have made my life a lot easier, though.

After reviewing the RTree documentation and finding some tutorials on how to compile a custom amalgamation of SQLite for iOS (not clear on all those details yet), it looks like RTree offers exactly what I need. However, the Spatialite extension seems to offer a lot more than just efficient virtual tables for indexing envelopes. I'm still trying to figure out how to turn the extension on in iOS, but if I can do that I think Spatialite is the route I'm going to take. Thanks for the suggestions!