Sorry to hear you had problems demonstrating you have the required documents to enter Canada, I would take legal advice on this.

My understanding is that you still have an ETA number, which was given to you in the letter of introduction. It is a shame you didn't keep a copy of this reference, but then hindsight is a wonderful thing.

I'm afraid your previous experience of what was accepted by BA or other carriers isn't much use at the time if BA were insisting on the ETA number, particularly if they discussed it with Canadian immigration who confirmed you needed the number; hope you manage to find a way to obtain it for your future travel.

Not sure how you figured BA have saved $600; was this the cost of your onward travel or the cost for the fuel for you and your travel for the difference in distance?

I would consider MCOL and see where you get to. Best of luck.