I'm glad someone is paying attention!
The thing to remember is that any position of the major scale can serve as any mode. You still need to memorize all the positions of the major scale. What I have explained in the answer that you sited was how the modes are actually USED.
Depending on which system of scale patterns you use there are either 5 patterns for what is known as the "caged" system, or 7 patterns for the "Van Eps" system (named for famed jazz guitarist George Van Eps). I teach the caged system to my students because it is easier to use and corresponds to the standard chord shapes as well as the pentatonic scales and all the standard arpeggio forms. I also use and teach aspects of the Van Eps system because they are extremely useful in connecting the various positions across the neck.
Once you have memorized the positions then it becomes very easy to use them as major or minor scales or as any mode you wish. For example: The A dorian mode as I explained it is the A minor scale with a #6th (A B C D E F# G A) This is how my EARS hear it but my HANDS are playing the G major scale! Try this with the progression Am7 to D7 (a Santana favorite) The #6th works well because it is the major 3rd of the D7 chord (F#). So I can use ANY position of G major over this progression and it SOUNDS like the A minor with a #6th!
Okay, lets try another one. Remember that the Mixolydian mode is the major scale with a b7. Lets use a very basic progression D Csus2 Gadd5 D (sweet home alabama etc.) The D mixolydian scale is D E F# G A B C D. So my ears are HEARING D major with a b7, but once again, my FINGERS are playing G major!
These are two basic examples of how we actually use and perceive the modes. We kind of have to separate the physical form of the scale and how we are using it. Use the two examples I have given and play the G major scale over the entire fretboard. You will begin to see that ANY position can be ANY mode, it just depends on the chord progression we are using it over.
The real truth is that the progression is based out of the mode. There is no C major in the key of D major so why does the D C G progression sound cool? That is because the PROGRESSION is based out of the Mixolydian mode! The same applies to the Am to D progression. There is no D major in A minor, so this progression is a Dorian based progression! This takes a while to get a grasp of so be patient and keep practicing!
Bonus question; You are not the only one who has trouble playing on the lower strings above the 14th fret. I think the main reason is that the frets themselves are just too damn small! It is hard to maneuver on those tiny frets unless we are using mainly the upper 3 strings!
Also, once you have memorized the 5 basic positions than you are just repeating them way up there.
Good Questions!! feel free to get a hold of me directly if you wish.