Mike,
  My plan A was to specify the beam positions.  However, the beam insists on 
staying horizontal regardless of the position override (probably for the same 
reason that it didn't work to simply giving the rest a pitch).

  Plan B would be to use hidden notes.  If we put them a bit earlier in time 
than the rest, there are no warnings, and the pitch of the hidden note can 
slope the beam appropriately.  Plan B opens up some horizontal space, but that 
might be a good thing around unusual notation.

I also made the first rest a r16*2/3 to squarely fill the first measure.
--
Keith


{ \override Staff.Stem #'stemlet-length = #0.60
  \override Beam #'breakable = ##t
  \relative c' {
    r16*2/3 \repeat unfold 40
    \times 2/3 {
%% plan A
%     \once\override Beam #'positions = #'(2 . 2)
%      f8[ g16\rest]
%% plan B
      f8[ \hideNotes a16*1/2 \unHideNotes a\rest]
%%
    }
  }
}


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