Re-printing instrument names

[Johnathan]

I am writing a vocal score that starts with 4 parts (staves), then adds a 5th
part later. I believe I've gotten Lilypond to do what I want in terms of hiding
staves, but I can't figure out how to do what I want with instrument names. 

I would like the 4 names to be printed before the first measure, which is not a
problem. Then, after several systems of 4 staves (the other one is hidden
because it contains only rests), with no instrument names printed before them
(shortInstrumentName is ""), the 5th staff is introduced. On the system where
that new staff first becomes visible, I would like to reprint all 5 instrument
names in front of the staves. The rest of the systems until the end of the piece
should show 5 staves with no instrument names in front of them.

Is there any way to accomplish this? Thanks in advance.