There are two schools in this matter. Pick what suit you best

1. Run parallel Tlog backups at the same time the reindexing is happening eg. Run a Tlog backup every 2 min while the reindexing is going on

2. Make a Tlog Backup, Switch the recovery model to Bulk_logged, perform the Reindexing, switch back to Full and when performing the next TLog backup do it on a drive that have plenty of space

Cheers,