(b) This section does not apply to persons conducting operations under subpart K of part 91
Note that it says "SUBPART K" which applies to fractional jet operators such as Netjets, it then goes on to say in 61.58C that 91K operators can conduct their own checkride, as can 121,135 operators.
So in reality this means that as a basic FAR-91 pilot you can do the 61.58 check in the 13th month.
As a FAR-91K pilot you can also do it in the 13th month but it wont be a 61.58 checkride.
As a FAR-135 pilot you can also do it in the 13th month but it will be a 135.293 (?) check ride.
You are stuck til the end of July as per 61.58(g)..... sorry.
Mutt