MATCHPROP can fix some of the characteristics of a newly placed table. I checked to see if a more robust match properties function might be possible and the necessary values that VLA-PUT-PROPERTY might have been able to set are all read only so I don't think that can be done.
I don't see any property that would obviously hold the Sheet Set linkage. It may not be exposed/available through the API.
The object data for my Sheet Index Table has these properties readable (those followed by (RO) are read-only and not available for PUT functions):
Select object: ; IAcadTable: IAcadTable Interface
; Property values:
; AllowManualHeights = 0
; AllowManualPositions = 0
; Application (RO) = Exception occurred
; BreaksEnabled = -1
; BreakSpacing = 0.605
; Columns = 2
; ColumnWidth (RO) = ...Indexed contents not shown...
; Direction = (1.0 0.0 0.0)
; Document (RO) = #<VLA-OBJECT IAcadDocument 0000000029ae4cf8>
; EnableBreak (RO) = ...Indexed contents not shown...
; EntityTransparency = "ByLayer"
; FlowDirection = 0
; Handle (RO) = "B7E3"
; HasExtensionDictionary (RO) = -1
; HasSubSelection (RO) = 0
; HeaderSuppressed = 0
; Height = 20.2292
; HorzCellMargin = 0.05
; Hyperlinks (RO) = #<VLA-OBJECT IAcadHyperlinks 00000000605f41e8>
; InsertionPoint = (20.1301 20.5586 0.0)
; Layer = "C-SHTS1INDX"
; Linetype = "ByLayer"
; LinetypeScale = 1.0
; Lineweight = -1
; Material = "ByLayer"
; MinimumTableHeight (RO) = 20.0825
; MinimumTableWidth (RO) = 0.58375
; ObjectID (RO) = 43
; ObjectName (RO) = "AcDbTable"
; OwnerID (RO) = 44
; PlotStyleName = "ByLayer"
; RegenerateTableSuppressed = 0
; RepeatBottomLabels = 0
; RepeatTopLabels = -1
; RowHeight (RO) = ...Indexed contents not shown...
; Rows = 80
; StyleName = "SheetIndex"
; TableBreakFlowDirection = 1
; TableBreakHeight = 12.1437
; TableStyleOverrides (RO) = nil
; TitleSuppressed = 0
; TrueColor = #<VLA-OBJECT IAcadAcCmColor 00000000605f7c60>
; VertCellMargin = 0.05
; Visible = -1
; Width = 5.12345
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