Rivqah,
What a wonderful book.
I would agree that the best course for preserving a desirable book book that is beyond repair is to copy the pages. If you feel the book contents have sufficient importance, you might consider scanning all of the pages and saving them, rather then copying/printing them. An inexpensive color scanner can provide at least a 600 DPI RGB image. (Most provide much higher resolution.) This process will require that you gently separate all of the pages from their binding, using an X-Acto knife at times.
I would scan all of the pages, including the cover page, tables of contents, forewords and introductions, and indexes. Scan them in color to retain as much subtle information as possible.
With these scans, you will have preserved the book. Not only can websites like Cyberhymnal make use of the files, but someone with imaging software like photoshop can clean up the pages and rebuild the book for digital printing if so desired.
A few of the more select pages from the disassembled book might make nifty gifts if they were mounted in a small frame behind glass for display in a home or office. :-)
Blessings,
MC