When tonicizing the mediant chord in the minor mode, you often use VII which acts as a secondary dominant of III and is very useful in tonicizing III if you are in the minor mode. Another option is to use vii˚6 of III which is the ii˚6 chord built on ^4. This would be vii˚6 of III. I can't really seem to find anything about the vii˚ of III. Is this a common chord to tonicize III or would you normally use a vii˚7 chord for this? I haven't learned vii˚7 chords yet but from what I understand, these are a direct replacement for V65 and would be built on the leading tone of the chord you are trying to tonicize.
I have not tried a survey of scores on this particular point, so this is a bit of guessing. You might not see analysis of, for example
Am: viio/III III, because it might get labeled as a modulation
C: viio I. Regardless of the inversion, I'm saying it might simply be analyzed in the relative major.
viiois not usually found in major, but fairly normal in minor. And my sense is I see that born out in real scores.