Another reason is that the EU (ECB, Council, Commission) public discussion focused on debt service and budget cuts rather than the substance of the "reforms" enforced at gunpoint, and not just the IMF research division but the IMF top leadership was more flexible on that.

This may be the reason why IMF was left out. Finance ministers fear debt cuts because they don't want to sell them to voters while compromizing on "reforms" won't cost them anything. Not having IMF in let them choose whether to compromize on debt or on reforms.