I think reporting out in the wilds is sort of a moot point let the NPC's do that.
Make the report button spawn a group of Storm Troopers (only in towns even player towns) They will ask the reported person to stand and prepare to be scanned for contraband just like they normally do on the spot. (this is a deep scan so will even look in your pit droid storage!) If the person starts to run away from the troopers, then we sort of know they are Jedi and have contraband on them this will cause very high visibility and worst if they start fighting with a saber in hand. you will get a reward for a good report ! (troopers will de-spawn after 5min of being on the ground)
If on the other hand the person stands and gets scanned, and it is found to be clean of contraband. Then the reporter gets a fine for false reporting. (credits to be determined) and the report button will not work for them for another hour so it can't be spammed.
What this will cause the jedi to do is really think and prepare before coming to towns and storing all their items. making them more suspectable to a BH attack. (BH if they have the jedi's kill mission the report will not work on that target, but it will work on the jedi's friends)
I could see more use of allies running into town for the jedi as a courier and this could actually open up maybe more job opportunities. Help wanted adds could be posted on the entertainer terminal for courier jobs so the entertainers have more options for side cash other then just sitting in the cantina all day.