If the Client (PM) rejects the proposed CE, what would be the correct steps to take?
re-notify it is a CE giving better/clearer reasons/demonstration why it definitely is a compensation event and see if they agree, and if still no go either to point 2 or 3 below
accept that they are right and give up and go and open a bottle of wine to console yourself
go to adjudication and try to get that decision overturned, and if you win open a bottle of wine to celebrate, or if you lose open a bottle of wine to commiserate (if you can afford one at that point)
Sounds like a wine/wine situation !!