Add/Delete/Modify files within a Disk Image (.dmg)? I know this may stem from a fundamental misunderstanding of the way disk images are intended to work, but even when full permissions are granted on a .dmg file, I am unable to add or remove files on the mounted disk image. Is there any way (natively or via a 3rd-party tool) to do this?

I know that when a disk image is mounted, a checksum verification is done, so I'm guessing that because modifying the image at all would destroy the checksum, this is inherently not allowed, but I'm wondering if there's a utility that could re-image the disk with a subset of its contents, perhaps recalculating the checksum in the process.

NOTE: Copying all the contents over, deleting, and then re-imaging is not a plausible option, due to the size of the image and the fact that it already fills most of the available space of the external drive on which it resides.
A disk image is designated as read-only or read-write when it is created. Simply changing the permissions on the DMG file will have no effect.

Here is one purported solution that I have not tried myself, that uses the hdiutil convert command to make a disk image writable, and hdiutil resize to add extra space if required for any additional content.