I'm going to have to agree with ESF on this. There's nothing that says that you can't fly a missed approach after you pass your DH or MAP. If you lose sight of the runway below DA or MDA, you have to go missed. It is true that the missed approach, and the obstacle clearance that comes with it, begins at the MAP, but it does not mean that you cannot join the missed approach after passing the MAP.
Take for instance a circling approach. If you lose sight of the runway while circling, you're supposed to make your initial climbing turn towards the landing runway and continue until you're established on the missed approach.
Now Gunnison is definitely a unique situation. The DA is abnormally high, and the missed approach begins a couple miles from the runway. I personally would circle over the airport, which I know for sure is protected airspace, and head outbound on the LOC until I reach the MAP, and then fly the missed as published. Flying the departure procedure would work as well, but unless you are familiar with that airport and have the departure procedure memorized, you most likely are not going to have it out in front of you. The last thing that you want to be doing is flipping through charts looking for a procedure and going missed at the same time with mountains around you.
That's my checkride answer. In real life, since the DH is more than 800 feet above the ground, and I'm assuming since I'm past the MAP that the weather is at least that, I'm just going to go around and fly a normal pattern. It seems much more practical and safer than trying to go missed. In regards to declaring an emergency and landing on a taxiway, I'm not sure I entirely agree with that. First of all, you better be darn sure that there is nobody on the taxiway, because if there is you're are going to have a really bad day. Also, even though there's sigmets out, you have to keep in mind that these are just advisories. It doesn't necessarily mean that there's severe weather at your location right now. Now if tower said that there are level 5 t-storms that just developed all around the airport, that's a different story. But if you declare an emergency just because of a sigmet, you're probably going to have some explaining to do to the FAA when you get on the ground.
This is definitely an obscure question, but it does a good job of making you think. It also shows the importance of preflight planning and maintaining situational awareness. And just as a side note, anyone who flies a low performance airplane into an airport with a elevation of 7673 feet, with mountains all around it, on an IFR day is just asking for trouble.