Trump is more like the MSM than typical internet trolls because he does not want to operate in anonymity and he is not trying to overturn the tables of any ideological agenda.
His best twitter partner is his critics because too many love to highlight false claims or inappropriate comments on the illusion of reducing his approval numbers when really all they are doing is making themselves feel better through misplaced compensation.
The problem with his tweets is lack of factual support and the best way to fight the barrage is not through ignoring, pleas of abandoning him, or clever roundabouts but rather one simple request:
Provide supporting evidence for the tweets
If we hit the MSM with a barrage of protests for running stories on tweets void of supporting evidence it would prevent his supporters from claiming we are trying to silence him and overall reduce the amount of energy on the issue because the MSM is largely guiding that buffet.
One unusual method with promise would be to simply agree with him whenever he makes obviously childish or bizarro allegations because it is the disagreement rather than the tweets themselves driving the energy. When he says he won the pop vote, just agree and it will give him no place to go. When he says he had the largest Inauguration crowd, simply agree and there is another issue knocked off the table.