Clearly the answer is #11, and there are two ways to see this. First (and most evocatively, I think) is the drug metaphor: the effects of the Ring are cumulative, and they also grow stronger in proximity to Orodruin. We can model the Ring as an involuntary opioid dispenser that is certainly harming Frodo's body cumutively. But, even more sinisterly, it's dosage is increasing in proximity to Mt. Doom. Clearly, if Frodo approaches Orodruin with high velocity, his "dose" of the Ring's power will become very, very high, and he will OD.
The second way to see this is a physics metaphor. In this case we model the Ring's action as a spring pushing away from Orodruin. Frodo uses his will to compress the spring. Each step he takes requires work. Frodo can only expend energy at a more-or-less fixed rate[1] (which is nicely called will power, and captures the same notion of work-over-time), so, as expected, his progress toward Mt. Doom slows considerably as the opposing force increases. (I would add that consuming nothing but lembas made the final leg of the trip even possible).
So, an eagle ride would have either a) resulted in Frodo overdose, or b) forced Frodo's mind to exceed it's capacity for work, snapping it and either killing him or letting the Ring take over.
The second way to see this is a physics metaphor. In this case we model the Ring's action as a spring pushing away from Orodruin. Frodo uses his will to compress the spring. Each step he takes requires work. Frodo can only expend energy at a more-or-less fixed rate[1] (which is nicely called will power, and captures the same notion of work-over-time), so, as expected, his progress toward Mt. Doom slows considerably as the opposing force increases. (I would add that consuming nothing but lembas made the final leg of the trip even possible).
So, an eagle ride would have either a) resulted in Frodo overdose, or b) forced Frodo's mind to exceed it's capacity for work, snapping it and either killing him or letting the Ring take over.
[1] http://psyserv06.psy.sbg.ac.at:5916/fetch/PDF/10978569.pdf