"forward across" can be used in written English.
You can use it to indicate motion in a certain direction. For example, "We walked forward across the grassy meadow."
But such epigenetic scratch marks are rarely, if ever, carried forward across generations.
Neolithic humans pressed forward across Europe and Asia.
Then he leans forward across the table, still half-seated on his bolted-down chair.
He leaned forward across his big desk as if he had something special to confide.
He leaned forward across the coffee table separating us and said emphatically, "The guy's a goner.
List leaned forward across the table and said, "That's what I'm interested in!
Intense and angry, he leans forward across the table to vent his frustration.
You need a reason to keep trudging forward across the frozen tundra.
This will link into work being taken forward across Government to ensure a comprehensive approach.
"I've taken on board the democratic arguments put forward across the Rhine.
He looks up and panics a little, calling again and hopping forward across the grass.
