I haven't done this in a while, but as far as I remember using one of the plugins in TGTools allows a system to be added or removed and didn't affect other systems. It's in TGTools Layout, split staff system and join systems. I wasn't using lyrics when I last used this, so I don't know how they'll react, but it's worth a look.

… One of the biggest time wasters in Finale occurs when you've done all your layout, but then need to move a measure or two, or create a new system in the middle of the piece, to improve spacing, improve page turns, use all available space, etc.....because all your manual staff spacing, lyric baseline edits, etc, are attached to the "system number", not the music itself …

Use the Page Layout Tool to insert a staff system.

In that way your manual layout edits will stay with the correct system.

The inserted staff system must contain at least one measure, but you can delete that extra measure when you are done.

Peter, thanks for that thought; that preserves measure flow and staff spacing (I think), but it doesn't preserve manually adjusted lyric baselines - those still get messed up everywhere past the insert point- and it doesn't preserve staff hiding (systems right before and after a change in number of staves get messed up). 

If it were Photoshop, the layers could be used for this.  I tried to use layers to add chord rows but couldn't.  Perhaps layers function could be tweaked.