I don't use it, but the experimental 'MultiPartDotPlacement' feature may help:!NoteWorthyComposer(2.5)
|AddStaff|Name:"Staff"
|StaffProperties|EndingBar:Open (hidden)|WithNextStaff:Layer
|Note|Dur:4th,Dotted|Pos:0|Opts:Stem=Up
|AddStaff|Name:"Staff-1"
|StaffProperties|EndingBar:Open (hidden)|MultiPartDotPlacement:Y
|Note|Dur:4th,Dotted|Pos:-2|Opts:Stem=Down
!NoteWorthyComposer-End
Note that it doesn't do anything unless the staff preceeding it has 'WithNextStaff:Layer'
Also for layered staves, 'Tie=Downward' can be used to force the dots downward:
!NoteWorthyComposer(2.5)
|AddStaff|Name:"Staff"
|StaffProperties|EndingBar:Open (hidden)|WithNextStaff:Layer
|RestMultiBar|NumBars:2|Visibility:Never
|Bar
|AddStaff|Name:"Staff-1"
|StaffProperties|EndingBar:Open (hidden)
|Note|Dur:8th|Pos:-1|Opts:Stem=Down
|Note|Dur:4th,Dotted|Pos:-2|Opts:Stem=Down
|Note|Dur:4th,Dotted|Pos:0|Opts:Stem=Down
|Note|Dur:8th|Pos:-1|Opts:Stem=Down
|Bar
|Note|Dur:8th|Pos:-1|Opts:Stem=Down
|Note|Dur:4th,Dotted|Pos:-2|Opts:Stem=Down,Tie=Downward
|Note|Dur:4th,Dotted|Pos:0|Opts:Stem=Down,Tie=Downward
|Note|Dur:8th|Pos:-1|Opts:Stem=Down
|Bar
!NoteWorthyComposer-End