My code is virtually identical to the following example:
https://github.com/iamamused/Example-MKLocalSearch.git
Here are the important bits:
I ended up giving up on Apple local search API and switching to Google. Their Place API is exactly what I needed. It finds relevant results quickly and up to 100k requests per day doesn't cost anything.
Auto-complete: https://developers.google.com/places/documentation/autocomplete
Details (need this for lat, lon): https://developers.google.com/places/documentation/details
With the help of JSONModel I built it into my iOS app in a few hours.
The results are exactly what I was hoping to see: