just recharged my batteries after finding them dead.

Now with neg cables detached from batteries, positive cables attached, key is off, everything off:
Voltmeter reads 12V between battery terminals
No voltage between positive terminals and neg cables,
but reads 12V between neg terminal and neg cable.
does that sound right?

 

Remove positive cable from battery.
Test for continuity between positive cable and ground/neg cables.

 

You need to test for key off amperage draw, not voltage.

With batteries fully charged, key off, remove the positive terminal and see what amperage is being drawn ( VOM set for Milliamps ) between the positive post and the terminal.

Shouldn't be more than 30 Ma if I remember right.

 

aftermarket radios and alarms can be power hogs.

 

Separate the batteries and test them independently. I had a draw I was searching for over a 6 month period, and it turned out to be a weak battery which I didn't find until I separated the batteries for testing.

Chris