I disassembled the max number every single day from day 5ish to day 50 and got LITERALLY no origin DNA besides the guaranteed one you get for the minotaur quest then got a game over because I had no salamanders. Great game design.
That's frustrating for sure, chance of getting Origin DNA should be a bit higher. Also, if you want to replay it and get it next time:
1. Make sure to upgrade Flora's 'DNA Acquisition Rate Up' and 'By-Product Rate Up' to the max first. (I guess you did that, but just to be sure)
I also noticed that Origin DNA is kinda 'locked' until Niel NPC unlock. Maybe I wrong, but just saying.
2. You can use 'the ultimate exploit' in the game while disassembling slaves/monsters - save at the moment you start disassembling. Wait and see if you got needed resources/Origin DNA. If there's a negative result - reload that save and wait again. This kind of 'reroll' works for other things in the game as well.
That's not optimal, but something you can use to your advantage.