OM's only data source is OSM itself and their volunteer dev team is already overloaded so that's the only option there for now (basically the same as with OsmAnd) but if you really want an OpenStreetMaps based GPS app with full address support ASAP you can try Magic Earth in the meantime. It's not FOSS, but at least it's not Google.
As for ice cream, it's a matter of checking to see if those closer businesses are mapped correctly or not. If they're properly tagged as "ice cream" in OrganicMaps but not displaying in the correct order then that's an OM bug to report, but my guess is that they're not entered properly into OpenStreetMap to begin with. Both are free open source projects though so we can make things better ourselves without begging a big corporation to do it for us.
Cheers!