MP3 archive file overlap and streaming with single encoder?

Hello,

I'm working on an audio archiver utility for a non profit radio  
station which uses liblame to archive 1 hour segments of audio at 3  
different qualities.  In addition I'm streaming one of the streams  
using libshout.

One of the features I would like to implement is file overlap, where  
the MP3 files overlap by 2 minutes, for convenience to listeners of  
the archives when a radio show begins early or goes over the hour.

I was curious if anyone knows if it is possible to use a single  
liblame MP3 encoder stream for file overlap and streaming.  I see that  
there is a lame_encode_flush_nogap which appears to be useful for  
creating a clean MP3 boundary.  Could this possibly be used at the  
beginning and end of the overlap (2 minutes before and after the hour)  
to start a new archive file and end the old one, respectively?  Would  
this freak out players which are listening to the continuous MP3 stream?

I suppose worst case is I have to use 3 MP3 encoders for the overlap  
period, just wanted to try and optimize things.

Thanks for any information on this.

Best regards,
Josh Green