Most USA airlines use 62 inches, not 61.
I am not familiar with your bike, so I have no idea if it would work, but I use the S&S Backpack. S&S also makes a hard case and I think that Co-Motion might also make their own S&S style case. These cases are 26 X 26 X 10 inches.
S&S Backpack is a soft case, but has stiff side panels. The four side panels at each end are strapped to each other with velcro, I find it works best if leave those a bit loose. I also made a center support for it out of wood, and in the flat top and bottom I added a sheet of Corroplast (from Home Despot) that I cut to 26 X 26 with rounded corners.
First photo, my S&S bike, second photo my Airnimal Joey folding bike. Third is with my bike packed in it, ready to hand to ticketing agent.
If you have not figured this out yet, last year Delta and American both implemented a new policy to waive oversize fees for bicycles in USA, so you could put a full size bike in a bike box and the fee was the same as for a regular piece of checked luggage. I am not sure if that policy also covers international flights or not. But, double check before you buy your ticket.
Southwest I assume still gives you two free checked bags, the photo above of my Airnimal was from a trip where I flew Southwest, my bike flew for free.
I have carried my S&S Backpack case as a backpack using the shoulder straps.