Here is one solution that is working for now. Using the Delphi Detours Library, adding this unit to the dpr uses list (I had to put it near the top of my list before other forms) causes the correct font size to be applied to the menu canvas, based on the form that holds the menu items in any popup menu.  This solution deliberately ignores toplevel menues (main menu bars) because the VCL doesn't properly deal with owner measured items there.
unit slMenuDPIFix;
// add this unit to the main application dpr file BEFORE ANY FORMS in the uses list.
interface
implementation
uses
  Winapi.Windows, System.Classes, Vcl.Graphics,
  Vcl.Controls, Vcl.Forms, Vcl.Menus, slScaleUtils, Math,
  DDetours;
type
  TMenuClass = class(TMenu);
  TMenuItemClass = class(TMenuItem);
var
  TrampolineMenuCreate: procedure(const Self: TMenuClass; AOwner: TComponent) = nil;
  TrampolineMenuItemAdvancedDrawItem: procedure(const Self: TMenuItemClass; ACanvas: TCanvas; ARect: TRect; State: TOwnerDrawState; TopLevel: Boolean) = nil;
  TrampolineMenuItemMeasureItem: procedure(const Self: TMenuItemClass; ACanvas: TCanvas; var Width, Height: Integer) = nil;
function GetPopupDPI(const MenuItem: TMenuItemClass): Integer;
var
  pm: TMenu;
  pcf: TCustomForm;
begin
  Result := Screen.PixelsPerInch;
  pm := MenuItem.GetParentMenu;
  if Assigned(pm) and (pm.Owner is TControl) then
    pcf := GetParentForm(TControl(pm.Owner))
  else
    pcf := nil;
  if Assigned(pcf) and (pcf is TForm) then
    Result := TForm(pcf).PixelsPerInch;
end;
procedure MenuCreateHooked(const Self: TMenuClass; AOwner: TComponent);
begin
  TrampolineMenuCreate(Self, AOwner);
  Self.OwnerDraw := True;     // force always ownerdraw.
end;
procedure MenuItemAdvancedDrawItemHooked(const Self: TMenuItemClass; ACanvas: TCanvas; ARect: TRect; State: TOwnerDrawState; TopLevel: Boolean);
begin
  if (not TopLevel) then
  begin
    ACanvas.Font.Height := MulDiv(ACanvas.Font.Height, GetPopupDPI(Self), Screen.PixelsPerInch);
  end;
  TrampolineMenuItemAdvancedDrawItem(Self, ACanvas, ARect, State, TopLevel);
end;
procedure MenuItemMeasureItemHooked(const Self: TMenuItemClass; ACanvas: TCanvas; var Width, Height: Integer);
var
  lHeight: Integer;
  pdpi: Integer;
begin
  pdpi := GetPopupDPI(Self);
  if (Self.Caption <> cLineCaption) and (pdpi <> Screen.PixelsPerInch) then
  begin
    ACanvas.Font.Height := MulDiv(ACanvas.Font.Height, pdpi, Screen.PixelsPerInch);
    lHeight := ACanvas.TextHeight('|') + MulDiv(6, pdpi, Screen.PixelsPerInch);
  end else
    lHeight := 0;
  TrampolineMenuItemMeasureItem(Self, ACanvas, Width, Height);
  if lHeight > 0 then
    Height := Max(Height, lHeight);
end;
initialization
  TrampolineMenuCreate := InterceptCreate(@TMenuClass.Create, @MenuCreateHooked);
  TrampolineMenuItemAdvancedDrawItem := InterceptCreate(@TMenuItemClass.AdvancedDrawItem, @MenuItemAdvancedDrawItemHooked);
  TrampolineMenuItemMeasureItem := InterceptCreate(@TMenuItemClass.MeasureItem, @MenuItemMeasureItemHooked);
finalization
  InterceptRemove(@TrampolineMenuCreate);
  InterceptRemove(@TrampolineMenuItemAdvancedDrawItem);
  InterceptRemove(@TrampolineMenuItemMeasureItem);
end.
One could just as easily patch Vcl.Menus, but I did not want to do that.