While Gizmo can cache a few files it doesn't really support downloaded files that exist on your phone, or are updated with playing stats that can be synced back to the MC Server.
JRemote2 doesn't support downloaded files yet.
Both require a network connection to the MC Server to update play stats such as [Last Played], [Number Plays], [Rating], because they aren't updating local files on the phone, but are updating the MC Server.
JRiver for Android would be the correct player to use, and it is supposed to support setting the Rating of Tracks. But actually I can't work out how to do that at the moment, and I have the option turned on. ??? If that worked, combined with the Handheld Sync functionality, you should get what you want.
Even when JRiver for Android is connected to a MC Server rather than running on its own local server, there doesn't appear to be any way to set the Rating, and it doesn't update any playing stats on the server.
MO 4Media supports downloaded files, but I just tried that with a fully licenced copy, and it didn't work. Even if it did, I'm not sure it would update the MC Server after the event when it reconnects to the server. If it updates the local versions of the files it should be possible to use Handheld Sync to sync playing stats from the MO 4Media downloaded files location back to the MC Server. I'm not sure. Ask in the MO 4Media thread.
I'm sure there are other Android players that update play statistics in tags on the local files on the phone, which could then be synced back to the MC Server using Handheld Sync. I just haven't used any for ages, so can't advise.
Hopefully someone comes along who can make a recommendation. Or you could just search the Play Store for a player that claims to update tags with playing stats and ratings.