OK, I have re-created the style as a linked paragraph and character style, but now my ".Find" loop never finds it!
With rg.Find
.Forward = True
.Format = True
.Wrap = wdFindContinue
.Style = "MyStyle"
allTheTips = ""

Do While .Execute
rg.Select()
... ' Processing happens here...
...
Loop
End With

I have given the new style the same name as the old style (which I have deleted). I am wondering if I have discovered a Word 'idiosyncracy'?!