What are you going to do if they turn you away at the last minute? If the primary purpose of the flight is to get to a bike tour you would be screwed.
I suggest that in the future you use more bike friendly airlines. I do so even when not flying with a bike. Why reward airlines that are hostile to bikes with your business?
That said, I have used a soft case that I am pretty sure gets down to the 80" limit for me. Mine is a cheap one with no padding and I add some cardboard. If I already had the ticket, I'd either use the soft case or ship the bike via bikeflights.com or shipbikes.com. You'd have to make arrangemants with a bike shop, warmshowers host,, or maybe a hotel/motel you wil be staying at to receive it.