"Would have had to have been" vs "would have had to be" for past event conditions
I would have had to have been and I would have had to be are alternatives, but have had already sets up the time reference, so the infinitive to be, rather than the perfect infinitive to have been is enough. Usage seems to confirm this. The British National Corpus has 15 records of would have had to have been and 45 of would have had to be. The figures for the Corpus of Contemporary American English are 38 and 67.
Speaking casually:
"I'd have to have been over 180lbs . . ."