Very doable with some claw grip and pause exploitation
The method: I had wedged the attack buttons down, controlled the sticks with my thumbs and would pause with my index finger (using a DS4). I'm able to get very clean and long streaks of ship overlap by buffering the sticks in pause at no less than full tilt. The caveat of perfect overlapping is that both ships can die to the same bullet... as I discover in stage 1-5
Levels:
1-1 - 0:00
boss - 1:39
1-2 - 2:24
boss - 4:38
1-3 - 5:35
boss - 9:13
1-m1 - 11:27
1-4 - 13:16
boss - 17:08
1-5 - 18:22
boss - 23:39
1-m2 - 24:37
1-6 - 26:36
boss - 30:34
1-7 - 31:30
boss - 35:48