Backup tool for pulling files out of encrypted disks?

The fact that your disk is encrypted is largely irrelevant. Whatever you use will need the encrypted disk to be opened (cryptsetup luksOpen ...) before operation.

I'll also draw your attention to e2image which may copy more filesystem meta data. It only works with ext2,3,4 file systems.

Besides e2image, your only real option is to look at tools which copy file trees rather than blocks. For backups, I use rsync copy files.

Besides files, what else does your system need?

Partition definitions will not be backed up with rsync. Partitions sizes can be listed with with fdisk -l <disk> eg: fdisk -l /dev/sda and stored this in a file somewhere for safe keeping.

To boot up, you system will probably use UUIDs to know what file system mount's where. These can be listed with blkid (sudo blkid).

If your system is using EFI (rather than legacy boot) then you need to also copy the contents of your EFI partition.