Greg is right, the 1407 is not meant to acquire non-standard images (like ones variable exposure). Also, it sounds like your Cohu camera may still be sending camera sync signals even when it is not triggered--basically black fields. This is why I think the acquisition in MAX looks like it's not waiting for the next valid field. What happens in MAX when you stop your grab pulses? You should get a time out error.
The cleanest solution from here (if you stay with a 1407) is to have the camera acquire in free run mode, and trigger the 1407 directly instead of the camera. This will cause some error in your timing since the 1407 needs to wait for the next valid frame from the camera once it received a trigger, but for a 30 frames per second camera, the error will onl
y be plus or minus 15 milliseconds. Not only will this give you predictable results, but it also greatly simplifies your wiring and coding.
Good Luck!
Kyle V