Yes fuel filter might be good to replace, although it may not resolve the issue.
But if you drained the tank significantly one time, it could be deep enough to suck in the residue.
Please check, or have a mechanic check, if there is anything wrong with the ventilation of the tank.
Are you using the official fuel cap or have you been using a different one recently?
Or you could pullover when it starts to do the stuttering and loosen the fuel cap a bit to make sure air can get by.
There is an output in the filler, and there should be some air hoses too I think, but I'm not sure how or where these actually run.
Another thought is the fuel return line, but that will probably not lead to this issue.