It sounds like your primary overflow may be undersized? How did your builder calculate the size pipe needed?
I know that after 5 years and tons of research (after building, duh) my #1 regret about my big pond is going with the smaller culvert. NRCS sized my pond as needing a 20" diameter, based on the 100 year volume calculation they used. I could either have gotten an 18 or a 24" diameter...I went with the 18 and have pretty much regretted it ever since. Biggest mistake I made on my pond construction...not the only one by far, but the largest.
As far as the emergency overflow, most folks I know just have a very wide spot cut out away from the levee to allow the really heavy rains a path to overflow that won't cause any cutting of the levee itself. Someone smarter than I will need to address whether there's any reason you can't just use another culvert as the emergency.