Diminished sevenths have the same issue to consider as the harmonic minor scales – that is, how to cover the minor 3rd (augmented second). I remember being fascinated to discover through one of my lessons with Edna Golandsky that a minor third over two black keys (eg. Eb-Gb) is slightly smaller than over two white keys (eg. E-G). For most hands, 3-4 over a black-to-black minor third is as large an interval as can be comfortably covered. Having the 3 on a black key and 4 on a white key over a minor third does not feel great, and 3 on a white key and 4th on a black key over a minor third feels even worse.
In 2009, I worked in consultation with Edna Golandsky and John Bloomfield to create these charts, along with the harmonic minor scales and dominant sevenths (coming soon!) The design for the diminished sevenths below places the 3-4 over the black-to-black minor third, the most comfortable option. Rather than change the fingering for different inversions, you can just use the same idea to maintain the spacing. Obviously, if you are beginning the first pattern from F#, beginning with a 2 makes much more sense rather than the 4.
The pattern that posed further difficulties is the final example at the bottom of the second page, covering D-F-G#-B-D. There is no comfortable fingering for the 3-4, which is why the 5 was chosen instead. Admittedly, this fingering requires a more sophisticated technique than stretching over a 3-4. However using shaping, lateral arm adjustment and a strong single from the 5-1 a completely convincing legato effect can be created, much to people’s surprise. In this case, I would give the students an option: they can stretch and use the 3-4, in which case I would introduce this diminished seventh pattern close to the exam to avoid practising it for an extended period of time, or develop the skills necessary for the 5-1 to work well.
To me, the more pertinent question than “What will the examiner say?” is “Why do we have to do this in the first place? Where in the classical repertoire does one come across this figure over four octaves?” In Mozart at the end of the A minor sonata (1st movement) the diminished pattern beginning on D features, but always within the span of an octave, and without crossing over the thumb. By the time the long flourishes up and down the keyboard appear in the repertoire, we are already in the romantic era and the pedal is usually on. If anyone can find an example in the classical repertoire of an extended diminished seventh over multiple octaves, I’d be very curious to know. Please do let me know!