Money speaks loudly. Compared to some of his other preparations it would be a relative cheap endeavor.
Considering most of the populace are not Darkfriends, then unless Gleeman have a higher propensity for darkness then average, most of them will not be Darkfriends. Darkfriends probably don't want to draw to much attention toward themselves, especially if that attention comes from the Dragon Reborn. If gleeman started spreading information that was contrary to what the DR had intended for them to spread it would be a good indication that they were indeed working for the Shadow.
People will continue to believe the worst of him unless they are told otherwise. Even then they might not come around, but there is no chance anyone will change their beliefs unless something or someone nudges them into thinking/believing something else.
Tell people a lie enough and they will start to believe it. Tell them a truth enough and they will start to believe it also, especially when you have the pattern working with you.

Then of course he could also have a bunch of letters printed and posted around the cities(printing survived the breaking), spreading the news he wants spread. The darkfriends wouldn't try to do likewise for fear of being identified and prosecuted.