I think all DMG's include a checksum. If you do a google search for "dmg checksum" you'll see a lot of help threads asking about an "Invalid Checksum" error when trying to open a downloaded DMG, so in theory a DMG should have the same integrity as a Zip and not need an external checksum, right?
I wasn't sure that every DMG has a checksum, and suspected they didn't, so I had to look it up.
The shell command 'hdiutil' is the command-line interface to the disk-image functionality. Its man page is here:
https://developer.apple.com/library/mac/documentation/Darwin/Reference/ManPages/man1/hdiutil.1.html
On that man page is this:
verify image [options]
compute the checksum of a "read-only" or "compressed" image and verify it against the value
stored in the image. Read/write images don't contain checksums and thus can't be verified.
verify accepts the common options -encryption, -stdinpass, -srcimagekey, -puppetstrings, and
-plist.
(Red hilite added.)
Based on this, I don't think a read/write DMG has a checksum. You could test this by running the 'hdiutil' command on the target Mac. If you need an exact command-line, just ask.
The reason you see "Checksum errors" on downloaded DMGs is that they're read-only or compressed.
You could produce a checksum by creating the DMG as read-only or compressed, but I suspect that's going to take about the same amount of time as making a zip file. You won't need to unzip on the target Mac, just mount the DMG (which verifies its checksum), and copy the files off the DMG.
The 'hdiutil' command also has a 'checksum' command, which can be performed on any DMG type. You could setup an Automator workflow to do this, show it to you, and then you run the same workflow on the target Mac and manually confirm.
If I were doing this rigmarole more than once a week, I'd definitely look into a sync app that handles it all for me. Even if it's only once a week, I'd probably get sick of it in a couple months and again look for a reliable sync app.