Hello DZoellnerFirst of all, if you keep enough fuel in the airplane and maintain the engine, the Lycoming engine is very reliable and a sudden engine failure is very rare.
Second, the Extra is built like a tank. Unless I had structural failure (not going to happen in an Extra, I can pretty much guarantee you that); or fire (again, good maintenance should prevent faulty wiring etc.); then I'd stay with the airplane.
Practice emergency landings. Cut the power to idle and glide in. You'll be surprised at how quickly the airplane comes down as yes, it does have a high sink rate. I practice these quite often. You have to pick your spot right away and go for it and stick with it....but you need to practice.
I've known of a couple of people who've had to make off field emergency landings, and both ended up ok. If you have to land in a field and can stop the roll out with a fence or something not too hard, you should be ok...plus if you're on grass or something like that, the airplane will stop fairly quickly.
I also carry a pretty heavy duty knife that is tie-wrapped to the tubing on the left side of my airplane where I can reach it, just in case I get upside down and need to get out.
Keep the airpane maintained well, lots of fuel in it, when going x=country, give yourself some altitude, keep your options open and it's your call ultimately, but I'd probably stick with the airplane myself.
Regards
Patty