Yes, I'm starting my answer with the supplemental reading, because in this case, the supplemental reading is amazing.
From a worldbuilding perspective, what you are designing is very similar to a Star Trek holodeck (or holosuite). Many of the stories focusing on the holodecks on Star Trek: TNG, Voyager, and the holosuites on DS9 are excellent sources of how their "safeties" work, how they malfunction, what the failure modes are, and why someone might want to override them (and how to limit access to that feature).
The Trekkie's trove of information, MemoryAlpha, has a page dedicated to this: Holodeck safety protocol
Specific Failure Modes
I'll go through each of your proposed safety measures and explore how they might fail:
Push the button on your VR watch
Electronics fail, mechanical buttons fail, power supplies/batteries fail, the signal from the watch might not reach the receiver. Maybe you fall in VR and break your wrist, and the watch along with it, and now you can't use the watch to get out and seek medical attention.
In Star Trek, this would be "Computer, Exit" or "Computer, Arch". Those voice commands failed frequently, for a number of reasons, but usually due to some malfunction in the computer, or a rogue AI taking control. It's important to note that when this type of failsafe fails, other related systems may fail as well, so it's entirely possible you find yourself trapped in VR with the other physical safety limitations malfunctioning as well.
OR simply close your eyes for 10 seconds.
Assuming your technology has absolutely perfect eye tracking and would detect this condition 100% accurately, my guess would be that the failure mode here would be users disabling that feature entirely, because it would be a pain in the butt. Imagine, say, enjoying a simulation of Beethoven performing his 9th Symphony only to close your eyes to feel the music... and... whoops. And with the feature disabled, users have one less failsafe keeping them from danger.
This one is good, if it is accurate, and adjusted for the baseline of the individual. It would need access to one's medical history, so as not to trip due to, say, tachycardia in someone who has a naturally high heart rate, or high blood pressure in someone with hypertension. Limits would either have to be very permissive, and trigger only on serious conditions, or users would have to deal with it triggering for benign "nuisance" reasons, such as momentary blackouts one might experience doing high-g flight training.
Privacy also needs to be considered, with medical history, notifications, and how those are transmitted.
Barrier around your body
Aside from the local gravity, this barrier might be the most difficult thing to pull off that you have suggested. Given the grey goo is already under perfect control, you might be better off putting all of the smarts into that. You can even protect against "passive" injury, such as the person tripping over their own feet and smashing their forehead into the corner of a table, by detecting the motion of the user and "softening" any objects they are about to collide with. This, to me, seems easier and more direct than introducing an entirely new force field system with entirely new failure modes. Especially since a typical sci-fi force field won't protect you from concussive brain injury in the above table scenario.
You can prevent the grey goo from entering someone's body by having it simply move itself away from/out of any orifices it may find itself in (or any new orifices it may be tempted to create). With the proposed level of tech, it would be trivial (and necessary) to 3D scan the body of the user in space anyway, so at all times the grey goo would know if a given coordinate in space is "inside" or "outside" the user.
You asked for better ideas. I think your ideas are generally fine, but what they lack is a hard, physical interlock. For example, in real life VR, you have the absolute ability to end the simulation by simply removing the headset. The software and hardware could be completely malfunctioning, yet that always works.
Your simulation is far more immersive, however, so any sort of physical interlock would take away from the simulation, and may be undesirable. Your VR watch is not an example of this, because it is still a "soft" exit, as it only sends a signal and relies on the software/hardware to do the right thing.
One way around this is to put someone else in charge; an observer on the outside that is responsible for stopping the sim on your command (or if certain parameters are exceeded). For a system this complex and large, it's likely it would be a staffed installation anyway. Obviously this person can fail as well, but so can you, if you are unconscious or otherwise incapacitated, so I judge it to be about the same risk. You probably need both exit methods. For example, you could have the location of the exit door always visible, like the "Exit" signs legally required in public buildings around the world.
It also couldn't hurt to set an absolute time limit for the simulation so the user doesn't die of thirst if all of the other exit protocols fail. You can make this malfunction-proof by running the sim off the grid and on battery power, so once the batteries are dead, the simulation stops. I suspect the energy requirements for this would be well into the megawatt range, though, so it's up to you if your universe has batteries with sufficient energy density to power this simulation for the required time.