Recently, I've gotten interested in learning how to transpose by sight. From what I've gathered, the most common methods have been to do by interval/position/ear.

One method that looks appealing to me is to change the clef:

http://derekremes.com/wp-content/uploads/Transposition%20by%20Changing%20Clef_by%20Derek%20Remes.pdf

It would basically involve learning 6 different grand staff positions and then juggling around the key signatures.

Has anyone trained themselves to do this before?
Obviously this would be a long term project, but not unfeasible.

What interval shifts are the most useful to learn or what are the easiest?

I was thinking of first learning the ones in which I already know at least half of the staff:

Up 3rd/Down 6th (Baritone - Bass GS)
Up 6th/Down 3rd (Treble - Soprano)

Being able going up and down a 3rd may also be the most useful when accompanying singers.

Next wold be these two since I would already know the Baritone and Soprano clefs:

Up 4th/Down 5th (Soprano - Mezzo Soprano)
Up 5/Down 4th (Tenor - Baritone)

Finally:
Up 2nd/Down 7th (Mezzo Soprano - Alto Grand Staff)
Up 7th/Down 2nd (Alto - Tenor)

If you take octave transpositions as requiring negligible thought, then the only extra clefs you need to learn for score-reading orchestral music are: Soprano - A, Tenor - Bb, and Alto - violas (D in Baroque and Brahms, maybe). Bass clef will do for E and Eb leaving (horns in)F/cor anglais which is probably worth just practising as transposition. The idea is that you learn the clefs not work them out on the fly.

John