All that's fine if the following implementation is also possible:
No such fallback is necessary, because the procedures of this SRFI are only applicable to objects that satisfy `nan?` and, as you point out, `real?`. I have added a paragraph in the Specification section emphasizing that these procedures are only to be called on objects satisfying those predicates. (I have also added calls to `assume` to catch complex numbers.)
If the implementation treats only some of the objects whose representation uses the bit-patterns of IEEE NaNs as satisfying `nan?`, so be it: they will satisfy `character?` or `fixnum?` or `eof-object?` or `pair?' or whatever, but not `nan?`. If the implementation is running on a Vax or an IBM mainframe (as is possible for Schemes that compile to C), then nothing will satisfy `nan?`, in which case the procedures should never be called at all.
Does that satisfy your concerns?