I'd add to this good answer, that I'm afraid, padding estimates gradually won't work — you are already working nights and weekends, and the worst — seems like you are expected to.

I worked in a similar environment for some time where I was expected to start my morning at 7am by joining a call with an offshore team and end my day at 11pm jumping on another status call. I could not fix it, this state of operations was enforced by management.

So many things are wrong here that I just don't believe you can change anything there either, you gotta find another job in my opinion.