Is it possible to stop the point of intersection being brighter by flashing the beams at a high frequency in a way that both beams will not be on at the same time?
Assuming that the distance to the intersection point of the beams is equal, you would have to toggle each laser on and off at the frequency of the time for light to travel twice the distance to the intersection. Secondly you would have to put the lasers out of phase. What happens is that for half a phase, laser one will be beaming, and for the second half of the phase, laser two will be beaming. A bit like traffic and stop signs.