Use of "couldn't have" to describe past lack of ability

Is the usage of "couldn't have" OK in the sentence below?

"With traditional training methods we couldn’t have completed the project on schedule."

It seems fine to me.

I agree with Jim.

Sure, I see no problems.

What annoys me is people who say "couldn't of" instead of "couldn't have".

What annoys me is people who say "couldn't of" instead of "couldn't have".

What annoys me is people who post the same moan twice.

.emit dnoces eht sdrawkcab tub eciwt naom emas eht tsop ohw elpoep si erom neve em syonna tahW