I think the problem is that you're not preserving the width of the text items, so they are only being given the width taken up by the rest you've entered. On the other hand, I don't think preserving the width will give a great result.
Try using hidden notes and rests together with the lyric editor.
Example:
Staff 1:
!NoteWorthyComposerClip(2.0,Single)
|Clef|Type:Treble
|Tempo|Tempo:88|Text:"Slow swing "|Pos:20|Visibility:TopStaff
|Key|Signature:Bb
|TimeSig|Signature:Common
|Dynamic|Style:f|Pos:-10
|Text|Text:"Solo"|Font:StaffItalic|Pos:8|Justify:Right|Placement:AtNextNote
|Rest|Dur:8th
|Note|Dur:16th|Pos:1|Opts:Stem=Down,Beam=First
|Note|Dur:16th|Pos:1|Opts:Stem=Down,Beam=End
|Bar|Style:Double
|Text|Text:"A"|Font:User2|Pos:13|Justify:Right|Placement:AsStaffSignature|Visibility:TopStaff
|Rest|Dur:16th
|Note|Dur:8th,Dotted|Pos:4^
|Note|Dur:4th|Pos:4
|Note|Dur:8th|Pos:1
|Note|Dur:4th,Dotted|Pos:-3
|Bar
|Note|Dur:8th|Pos:0
|Note|Dur:4th,Dotted|Pos:1
|Note|Dur:8th,Triplet=First|Pos:-1|Opts:Stem=Down,Beam=First
|Note|Dur:8th,Triplet|Pos:0|Opts:Stem=Down,Beam
|Note|Dur:8th,Triplet=End|Pos:1^|Opts:Stem=Down,Beam=End
|Note|Dur:4th|Pos:1
|Bar
|Note|Dur:8th|Pos:1
|Note|Dur:4th,Dotted|Pos:-3
|Rest|Dur:4th
|Note|Dur:8th,Triplet=First|Pos:#-2|Opts:Stem=Up,Beam=First
|Note|Dur:8th,Triplet|Pos:-1|Opts:Stem=Up,Beam
|Note|Dur:8th,Triplet=End|Pos:n-2|Opts:Stem=Up,Beam=End
|Bar
|Note|Dur:4th,Dotted|Pos:b-4
|Rest|Dur:8th
|Rest|Dur:4th
|Rest|Dur:16th
|Note|Dur:8th|Pos:-3
|Rest|Dur:16th
|Bar
|Note|Dur:8th|Pos:0
|Note|Dur:4th,Dotted|Pos:1
|Note|Dur:8th|Pos:0
|Note|Dur:4th|Pos:1
|Note|Dur:16th|Pos:-3|Opts:Stem=Up,Beam=First
|Note|Dur:16th|Pos:-3|Opts:Stem=Up,Beam=End
|Bar
!NoteWorthyComposerClip-End
Staff 2:
!NoteWorthyComposerClip(2.0,Single)
|Rest|Dur:4th|Visibility:Never
|Bar|Visibility:Never
|Note|Dur:Half|Pos:0|Visibility:Never
|Rest|Dur:Half|Visibility:Never
|Bar|Visibility:Never
|Note|Dur:Half|Pos:0|Visibility:Never
|Rest|Dur:Half|Visibility:Never
|Bar|Visibility:Never
|Note|Dur:Half|Pos:0|Visibility:Never
|Rest|Dur:Half|Visibility:Never
|Bar|Visibility:Never
|Note|Dur:Half|Pos:0|Visibility:Never
|Rest|Dur:Half|Visibility:Never
|Bar|Visibility:Never
|Note|Dur:Half|Pos:0|Visibility:Never
|Rest|Dur:Half|Visibility:Never
|Bar|Visibility:Never
!NoteWorthyComposerClip-End
Staff 2 properties should be set to Mute (or just mute all the notes), and all the Staff 2 notes and rests should be hidden.
Now add chord symbols as lyrics to staff 2. While in staff 2, press Control-L, then number of lyric lines 1, alignment top, and add the chords:
F C7 F F7 Bb
They'll line up with each hidden note in Staff 2.
Layer the staffs.
You'll need to use ascii characters to get the hyphen if you need chords like Cm7-5 or F°
I think you'll find the result satisfactory.