I fly into airports surrounded by high terrain on a regular basis. I suspect some of the answers here come from pilots who do not.
Staying on a SID will not protect you if you lose one engine, not during take off, not during MISAP from above or below minima. It MAY be OK, but you don't really know.
The MISAP procedure will protect you in the event of a single engine MISAP from minimums. It is designed to do this, and if you have terrain issues you will have different minima depending on your weight/performance. You need to check this during planning, and if needed, the weight must be limited.
If you go around from below minimums on a single engine you need to stay on your take off E/O procedure. And. yes, I have this procedure available when I fly into any of these airports. It doesn't say anywhere that I HAVE to, but my @ss is in the aircraft, and my objective is to keep it safe.