I find nothing particularly objectionable in the G-sharp — tritones were not unheard of in the seventeenth century (and this is just a diminished chord extracted from the dominant seventh). Indeed, in the arrangements Psalmody for a single voice... by William Carridge, this is presented as a first inversion dominant seventh chord (the bass line B and subsequent C-sharp replaced by G-sharp and A, respectively).

Changing it to an F-sharp (in the resulting B minor chord) softens the feeling of the accented syllable and, while perhaps acceptable, isn't quite as harmonically strong as leaving the G-sharp as it stands.

Are there any other sources for this tune and harmonization?

I agree completely, Adam. For those who don't have a keyboard handy, I'm attaching an MP3 of this harmonization. The more I listen to it, the more I like it!