I think you will find that online blind prices are better than box stores. If you have a local blind franchise, they may be able to cut you a deal too. The online people will cut blinds to fit exactly as you instruct them.
I would call customer support and ask them what they might suggest for your situation. They have probably encountered it before.
One thing that came to my mind is that the hardware for a horizontal blind that wide better be robust because the things is going to end up quite heavy. I would break the space into sections. Or think again about verticals.
Shutter type window treatments might be another possibility for all or part of the window and might break it up more logically.
And you are sure you could not make some very informal, not pleated, drapes work? Pier One and IKEA have nice, simple airy cotton ones. You can make drapery hardware for them out of PVC pipe and lhooks and screw anchors. Paint the PVC if you want with Krylon Fusion. (An interior designer turned me on to the trick ages ago). You can also use wire or cable systems for almost invisible hardware.
Also, IKEA has some nice window treatment systems that move on ceiling tracks as random panels. They look very contemporary, free form and nice and do not have that pleated drapery look I hate either. I am thinking by going with something more random, it might look better than if trying to fit sections over that 119" span. Like this: