Once you convert the labels to annotations they are no longer labels and therefore not governed by the Maplex engine, so none of the placement options or rankings (including the background label setting) have any effect.
When you convert labels to annotation in a database, they become another feature class and are stored separately from the mxd. If you convert labels to annotation stored in the map (and note if your mxd corrupts, your labels and all that placement work are gone), they are converted to graphics - essentially a text box in the data view. The text box is part of an annotation group which has some properties you can control from the Annotation Group tab on the dataframe properties dialog.
I believe (though I can't cite it at the moment) that labels draw on top of graphics and graphics draw on top of data layers. Annotations don't draw above labels, but labels try to avoid overlap with them (and other graphics) if not forced per the never remove option.
Probably the easiest solution to your problem is to:
- Either copy an existing annotation or create a new one using the text box tool on the Draw Toolbar (possibly with a new annotation group if
not the default one - you have to pick on the Drawing drop-down
- Format it the size/color/etc you want it and move it into position.
- Right-click it, choose Order, and then Send to back.
It should then be behind all your other annotations but still on top of all your features.