A belated welcome to the forum. I have a dug and dammed 1.25 acre pond near Watkins Glen. Have you seen the water flow in your dry creek bed during spring runoff? With 20 acres and 1” of runoff, you might have 72600 cubic feet or 540,000 gallons or water coming in from that dry creek. This would give you the equivalent of 26” of water in your 0.75 acre pond that your spillway would need to handle (spread out over say 24 hours or so so maybe a few inch rise). Up your way I think you get an occasional 3+ inch rain event and Agnes dumped almost a foot so I would just consider the width of the spillway and the maximum historical volume of water you could have to deal with.
I control the flow into my pond (
inlet control) but even so have seen the level rise to 4-5” above full pond during a significant rain event. My spillway has a lower section about 6’ wide that gradually rises as it widens to 15’ wide. Since I have a dam I needed a secondary “emergency” spillway that is 6” higher in case we have an “Agnes” event or if the beavers come while we’re on vacation. I have a fabric and stone lined spillway as they are proposing and it seems to work so far. Just keep the potential volume in mind. The ultimate level of the pond seems to be set by the level of fully compacted clay under the fabric and not by the stones on top. Water seems to run along the fabric just fine. I have tried to add a picture during a typical rain event.
The 12” culvert may be OK but you may consider 15” if there is any debris that could be carried downstream to that point. I have a 12” culvert that occasionally overflows if twigs get in the way.