1st try: 'she would have had to keep the volume down though'
2nd try: 'she would have had to have kept the volume down though'
i think the first one is right. saying 'would' implies hypothetical, so shouldnt the rest match? I think 'had to keep' sounds like it also implies something that hasnt happened so it works better with 'would'
'had to have kept' sounds like it refers to something that actually happened which doesnt fit with 'would'
i dunno, im no expert. youre from england arent you?