If I have a 2nd stage free flow problem in warmer water, depending on depth and need/desire to do a safety stop
Assuming we are talking about recreational diving and not at trivial depths. For the purposes of general advice, I would just make my contingency plan such that I don't have to eliminate any other safety protocols in the event of a gear failure. People often bring this up in the context of the endless pony size discussions - they say "I always do a safety stop, but if I had an emergency I wouldn't do one". My response "why not just set yourself up so that if you have to ascend due to failure of your primary gas supply, you can still do the stop since you thought it was worth doing on all of your other dives?"
I would either switch to the octo on necklace under my chin and head skyward
The only use of an octo for a single tank diver is if there is a problem that only affects your primary regulator and doesn't involve a gas loss. That is - failing closed or lost mouthpiece. Failing open (i.e. unstoppable free flow) or hose leak means that the octo isn't going to be good for long, especially if it happens in the later part of the dive.
I appreciate your post as it made me think through my protocol again, and there is always occasion to reflect on this.
-Z
Now THAT is a thinking diver! I also really enjoy these discussions, and I often learn things from them.