One option would be to spend a day in Frankfurt without the need to reissue the ticket at all.

You could take the LH flight from CDG that leaves at 9.10am and arrives at 10.25am. Then you could spend the day in Frankfurt, and the following morning take either the SQ flight (at 8.30am) or the first LH flight (at 10.05am). With a lass-than-24hr connection, you've got a transit instead of a stopover, and you've also got virtually a full day in Frankfurt.

In addition to saving the re-issue fee, you also save the significant hassle of getting a new itinerary approved and priced -- to me, that's worth as much as the re-issue fee.