My recommendation is this:
Don't let budget get in the way of doing this "right"...whatever that is. Anything less is likely a bandaid.
When that water control system was designed, there was a reason. If you can contact the original designer of the system, or your engineer understands it, I'd look at the best way to fix it.
A siphon might work, but will it handle the volume of water that comes during high flow?
Will the elevation of water during a flood event compromise the lowest point of the dam? If any of this is a concern, I'd sure look at other options. If you use an engineer and follow his recommendations, and use a reputable, bonded contractor, you have confidence...and recourse.
