I have a title off of a 1951 suburban and it also states sta wgn on it. The tabs were also stamped with a unique number. I have never seen the DMV hassle someone over the tab number though.

Do you have the original 1951 black and Yellow plate or a 1963 Black and yellow plate? Most likely you have the 1963 issued plate without the tab, unless this was a barn find that sat for 57 years.