I have experienced this as well, the performance degradation of DFA to NFA is enormous and while not as bad as exponential backtracking, it's close to ReDoS territory.
The rust version of the engine (https://github.com/ieviev/resharp) just returns an Error instead of falling back to NFA, I think that should be a reasonable approach, but the library is still new so i'm still waiting to see how it turns out and whether i had any oversights on this.
Here RE2 does not fall back to the NFA, it just resets the Lazy DFA cache and starts growing it again. The latency spikes I was mentioning are due to the cost of destroying the cache (involving deallocations, pointer chasing, ...)
The rust version of the engine (https://github.com/ieviev/resharp) just returns an Error instead of falling back to NFA, I think that should be a reasonable approach, but the library is still new so i'm still waiting to see how it turns out and whether i had any oversights on this.