And just to clarify, in case I seemed to perhaps be suggesting differently, I think the writing is Furth's. Another thing that I perhaps should have mentioned in the earlier post is that of the five productions (at least that I know of) for which Sondheim and/or Furth were around making changes until they finalized things (at least to the point of deciding that they had a new version that they wanted to license), only the first was directed by Lapine. It wasn't till nine years after the La Jolla production (the one directed by Lapine) that they decided their work was basically completed. And major changes were made in at least two of those four productions (as discussed in the transcript I linked elsewhere). Even between Leicester in 1992 and the York in 1994, there were changes to some of the dialogue, although no major structural or character changes.
Of course, they may well have been consulting with Lapine all that time. I don't know. Perhaps we will learn more one day (although I fear that what we will read will mostly be memories, which may not be all that accurate).