What can I do to (a) make clear to my boss that I'm on the verge of resigning over these issues (b) that he has to fix this, with the solutions I have proposed to him in the past or with some of his own ideas.
Your projected outcomes are unrealistic. Neither of these will eventuate. They're not happening for your colleagues, your predecessor or you.
my now-boss walked me through a completely different part of the
office...His primary solution is to assign everyone less work to
account for the "distractions".
Your boss is a deceitful moron and deserves none of the respect and restraint you have so far shown.
I would normally advocate communication and everything suggested by Sourav Ghosh, but in ...
Healthy workplace == Healthy and Motivated workforce == Productivity. There is no two things about it.
Bring it to the notice of your superiors immediately (this time officially, by setting up a proper meeting through email invite, for example). After all, it's your organization's responsibility to provide you with proper working conditions. If you ...