Keyboard range in W. F. Bach

I started to revisit W. F. Bach Klavierfantasien. I have the Schott Edition 6122, dated in 1972, ed. Peter Schleuning. About the Fantasie No.2, Falck 17, Schleuning writes that it was composed when the composer was in Dresden, where he lived 1733-1746. If so, it is surprising that the range goes up to f#‘’‘, which at the time was very rarely reached by keyboards in German lands (range up to g’‘’ was typical of English spinets and Spanish keyboards). IMSLP

One possible explanation is that it was meant for a clavichord. Among an online list of anonymous clavichords, there are about 70 that are German, and one (only one …!) of them reaches g’‘’. Problem is, although many later Fantasies by W. F. Bach are clearly meant for the clavichord, this one looks very much as harpsichord music.

Another possibility is just that the dating (supposedly based on style as the source of these Fantasies are undated copies) is wrong.

Any ideas?