Do you typically have so much water that a "slightly leaky" dam still holds the water level of the pond at an acceptable level?
If so, perhaps you can do the repairs yourself, if it doesn't have to be perfect.
One improvement compared to 50 years ago, might be to add a vertical strip of pond liner material behind one of your courses of stones. Perhaps that would lower your leak rate and make the stones less likely to shift if the dam is mostly holding equal pressure across the face.
Also, if you are considering a siphon, then you might consider a permanent siphon. That would be useful for your short term problem, would allow you to mostly drain the pond for your dam repair, and give you more pond outlet capacity as some protection against future big rains.
Here is a link to an automatic siphon system so you can see the concept.
Siphon System with automatic levelP.S. If you can send pictures, then some of the actual construction experts on the forum might drop into your thread with some good advice.