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I think your method with visualising a guitar isn't too bad. Like Dan Gilbert I come from the piano, so I always automatically see a piano keyboard when I read intervals and it becomes instantly clear what inverval it is. The guitar has the downside that it's not quite as visually simple as a piano keyboard (which has the advantage of looking the same in every octave), but I think with practice you can do that quite as well on the guitar. But with time you will also internalise the five-line note system to such a degree that you immediately can read an interval by considering how many semitone steps lie between them, diatonically, while leaving out sharps and flats first:
No semitone step: maj. 2nd, maj. 3rd, aug. 4th
One semitone step: min. 2nd, min. 3rd, nat. 4th, nat. 5th, maj. 6th, maj. 7th
Two semitone steps: dim. 5th, min. 6th, min. 7th
Then augment the interval by a step for any sharp on the upper note or flat on the lower note, and diminish it for sharps on the lower note and flats on the upper note. (Natural signs can count as either "sharps" or "flats" depending on they key signatures.) For example, in C-major you'd directly see about the interval Bb-D that between the two "noteheads" B and D there is one semitone step which would make it a minor third, but you then increase this interval by one because of the flat on the lower note, making it at major third.
I don't think however that this method will be faster than your guitar-visualisation, so just use what works and use it over and over again till you're fast. After enough time you will have seen, say, the interval F-B so often that you instantly translate this note-image into "diminished fourth". The method of getting there doesn't matter a lot in the end.
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