rebuilding indexes and logshipping?
My first suggestion would be to use intelligent re-indexing rather than just blindly re-indexing everything. This will help to minimise the impact on the logs un-necessarily. Ola Hallengren's offers one such solution.  See http://ola.hallengren.com/

External storage on a SAN that uses either cheap discs (SATA), or dedupe technology, makes it more affordable than expensive SAN discs.

Increasing the frequency of the log backups,and the copy and restore operations, makes sense to me. Ensure the maintenance is out of hours so that any learning curve about capacity minimises any pain.