The Windows keyboard does actually implement something similar to your first and third suggestion. You can spell words by fixating on the first letter of a word, glancing between the following letters and finally fixating on the last letter. Some people can do this to successfully and achieve good input speeds, however, it is a skill that takes some mastery.
For me the real problem comes from three places.
Firstly, having to spell out words either with some kind of keyboard or even with a Dasher-like system means word length matters, long words are harder to enter than short words. The amount of effort needed to express an idea should be proportional to how unusual that idea is, not how many letters are needed to express it; "Hello Dave, nice to see you, how are you today?" should be easier to write than "Eel shoes".
Secondly, in order to achieve some level of throughput, you need to accept that you're going to be living near an edge where typos are inevitable. On current systems, the mechanisms for making corrections are extremely disruptive to throughput, mostly involving repeatedly pressing a key to delete the last character, word or sentence.
Thirdly, similar to the second issue, revising finished text is also a fraught problem that is inadequately addressed and often requires repeated pressing of arrow keys and the like.
I am working on a solution that I believe addresses all of these issues. A solution that allows text to be created quickly using input methods slower than typing, be it eye tracking or switch access scanning. Similarly, a system that allows the same input methods to be used to review and revise text efficiently.
I will be looking to see if I can take advantage of Paul's interest in this area to help his friend and others.