One note on all this, based on personal experience (board member for a number of years, president for 2 terms in a small HOA).
When firing the management company, ensure everything is done in writing. If there isn't a paper trail, it won't count. The only reason I bring this up is because of the verbal arrangement your HOA president had in place to do thousands of dollars of work - don't let him get away with foolish practices like that again.
If you can prove that the management company was paying bills late when money was available, you may be able to fire them for cause. The contracts we had with management companies usually required a 60 to 90 day notice for contract termination due to convenience. I also believe that they included a clause that would allow them to be fired immediately for cause. However, before jumping in and not giving them notice on these things, I'd contact your association's attorney first. If s/he agrees that they can be fired for cause, it would also probably be worth paying the attorney a couple hundred bucks to write the letter terminating the contract.
I wish you the best of luck on this. While you've got 4 others on the 7 member board on your side, it might also be a good idea to see if your bylaws would allow members to vote on a motion to change the Board's leadership to prevent things like this from happening in the future.