Here's what I came up with that should do what you need. It is a modification of the RhythmicStaff context with your settings as I understood them:
\version "2.18.2"
scale = #-3
\layout {
\context{
\type "Engraver_group"
\name "RhythmicLine"
\alias "Staff"
\override VoltaBracket.staff-padding = #3
\override Stem.neutral-direction = #UP
\override Beam.neutral-direction = #UP
\consists "Output_property_engraver"
\consists "Font_size_engraver"
\consists "Separating_line_group_engraver"
\consists "Dot_column_engraver"
\consists "Pitch_squash_engraver"
\consists "Axis_group_engraver"
\accepts "Voice"
\defaultchild "Voice"
\override TupletNumber.font-size = \scale
\override Stem.font-size = \scale
\override Flag.font-size = \scale
\override NoteHead.font-size = \scale
\override Rest.font-size = \scale
\override NoteHead.style = #'slash
squashedPosition = #0
\override VerticalAxisGroup.staff-staff-spacing =
#'((basic-distance . 0) (minimum-distance . 2) (padding . 1))
createSpacing = ##t
\description "A context like @code{RhythmicStaff} but for printing rhythms.
Pitches are ignored; the notes are printed as slashes without any staff lines."
}
\context {
\Score
\accepts "RhythmicLine"
}
}
\score{
<<
\new RhythmicLine { \repeat unfold 2 { c4. r8 c4. r8 } }
\new Staff \new Voice { \repeat unfold 2 { c'4 d' e' f' } }
>>
}