As it frequently happens, I am giving advice to someone with far more expertise on the topic than I have!
Having water overtopping the dam certainly answers my question about your main concern for your lake. I am glad you survived that frog strangler without damage to your dam.
I am sorry to hear about the damage to your emergency spillway. However, if it took a 50-year(?) rain event to damage it, then you might have the "proper" amount of protection for your pond. The budget for building a perfect system is always much higher than for just a 98% good enough system.
Another affordable option might be to raise the freeboard of your dam? You do have a huge capacity to pass water. If you could compact a few more lifts of material across the top of the dam, you might prevent over-topping for a 100-year rain event.
P.S. When I was talking about "automating" your flood control pipes, I was only using that term in the loosest sense. I have utilized automated/remote control valves in high pressure gas pipelines. They are an awesome technology, but they are expensive and they are NOT idiot proof. In my experience they are more likely to fail or perform poorly in the extreme conditions when they move out of their normal operating envelope. (Just when you need your automation the most.)
The flood control project around my city that I have observed for many years has hundreds of flood pipes with the outlet swing gates as I have described above. I very rarely see any required maintenance performed on them. I believe they were installed in the early '70s. That is a lower level of "automation" that might suit your needs. Those gate valves on your flood pipes are huge. The motors to move them automatically will necessarily be very large.
If you are already doing concrete repairs for your spillway, could you buy yourself some more freeboard by cementing in a large siphon within the emergency spillway. You could set it up to automatically start siphoning at your desired pond elevation. An 18" siphon pipe (for example) would be moving a lot of water at full siphon prior to peak discharge from the creek reaching your pond. Would that be enough to preserve enough freeboard that your dam does not get overtopped? It would certainly be much cheaper than a full chute type spillway.
Just throwing out more ideas for you to chew on since you understand all of the physical forces involved AND have eyeballs on your actual project site.
