I just ran a build using _input and InputEventScreenTouch. The results were very similar and the controls were still laggy by just enough of a margin to make it hard to play.
This was the code I wrote:
func _input(event):
if event is InputEventScreenTouch:
#check if its left or right side of the screen when pressed
if event.position.x < 144:
touch_left = true
else:
touch_right = true
if event.is_pressed() == false:
touch_left = false
touch_right = false
It seems like Godot is having trouble registering a quick tap input. When I tap my screen the input event doesn't get called.