Some of those you've spoken to have advised you it may look better for you - in the event that he seeks PR through court - if you had put him on the BC.
But you have a couple bullets for your gun as to why you felt it was in advisable...... Namely that he went missing on three day drinking benders around the birth, and that you have had to try to prevent him from drink driving.
What were the dates of those incidents. Can you pin point the dates of the drink driving?
You need to note dates if you can and discuss it with HV, Women's aid etc.
You were anxious/had huge reservations about him getting unsupervised access to the baby due to his behaviour around alcohol.
One would think that would affect the judgement of legal authorities re. you not willingly giving him PR. It would certainly affect mine if I were involved in a case.
Make sure it's noted and logged with anyone you speak to, ideally with dates.
He can't prove you wrong, he can say you're lying, you can respond that he's lying. The information will stick in people's minds whether he claims you're lying or not.