My Z eats batteries - help!

I doubt if the ground strap has anything to do with it, but have you disconnected it to see if there is a difference? One good way to check for shorts or leakages is to connect an ammeter in series with the battery cable and see what kind of draw you have with nothing turned on. Just sitting. If there is a draw then go to the fuse box and start pulling fuses one at a time until the draw drops to zero (may have a small draw from the clock but not enough to discharge in a short time). When you find the fuse that clears the current draw, you then have the circuit, or circuits that need to be checked for frayed wires. Not likely to be anything on ignition or accessory circuits. Most likely items on BAT circuits like lights. Might possibly be an alternator or regulator. Easy way to check them is to disconnect and see if there is a current drop also. Possibly a leaking noise condensor on the altenator also. Just disconnect it to test. Make sure you don't disconnect the altenator main wire while the battery is hooked up. Just unhook bat then the alt wire then reconnect the battery and your test connections. We don't want big sparks flying do we?