How often do other teams make offers to a player on a non-exclusive rights tag?
Looking at a history of tagged players since 2015, I found 1 that was traded and 3 that signed long-term deals w/ their original team. This doesn't count Davante Adams who told the Packers he wasn't playing under the tag - period. Most played the year out on the tag.
There is little evidence to suggest that the tag is a positive thing for a team.
So, to answer your question, I would have had them let him walk. Bad business? Maybe. But this team has enough distractions as it is. We don't need a guy with Payne's attitude about getting paid hanging around on the tag.
Now, if we manage to trade him for value in this year's draft above the compensatory level we would get for letting him, great. But do you really see this front office being that savvy?