Do you flick once he's stopped? Try to watch for signs that he's going to stop and encourage him forward with a snap of the whip before he gets his head down. Once they get the idea that they can stop, it can sometimes be harder to get them to move or push them on at a decent, consistent pace.
I have a horse which thinks of his belly during lunging sessions too, only he doesn't get back to work grudgingly, he shoots off at an yucky rough trot for a few laps
, so I need to give a smaller pop before he stops to keep him working nicely.
If he's not keeping himself going without making grabs for the grass within a few sessions of consistent correction, I'd have nothing against putting a daisy rein on, but still keeping up with popping the whip the second he makes an attempt to stop for a snack! That way the daisy rein is only there for back up if he thinks he's starving and ignores your signal to get moving.
Another thing is if he has a small forage based feed before work, he might be less inclined to try gobbling grass during work time?
Good luck, hope you sort something out