I know this article is a bit stale, but I hope this helps someone:
Just had to do this same thing in order to save space on backups. It actually wasn't difficult at all, provided you have some time and an extra SD card.
I started by creating a script that backed up everything I was interested in. Credit goes to this article for getting me started. I think rsync pushing to a remote machine would be better suited for this, but I had enough space on the original SD card to go this route. I can provide instructions for rsync too needed. Rsync supports exludes also, just exclude the same directories that the following script excludes.
tar -zcvpf /backups/fullbackup.tar.gz --directory=/ --exclude=proc --exclude=sys --exclude=dev/pts --exclude=/etc/fstab --exclude=backups .
Next, I installed Raspian on the spare SD card, then moved the backup over to the new card. To restore the backup, I ran
tar -zxvpf /fullbackup.tar.gz
If you use rsync instead, you could probably restore a backup remotely, if space on either SD card is a concern.
NOTE: I didn't exclude fstab, and the article I linked doesn't mention to do so. Because NOOBS has a different partition map, it failed to boot. I just plugged the SD card into another linux machine and edited fstab to point to the proper partition. But if you follow the above steps, you shouldn't have to do this.