Do you know what would help with that? Look at the non-bloc candidates who are running, and get people to vote for them.
The only way to break the power of a bloc vote, is to dilute it.
And good news! the CSM elections using a Wright STV system, which means if the first candidate you vote for doesn’t get enough votes to survive an elimination round, your entire vote moves to your next candidate (who hasn’t been eliminated) So you don’t even need to agree on the order of votes, as long as you put them all down.