Remove bridge, make the string holes deeper (avoid drilling through body), refit bridge. When stringing up, place spacer nuts / old ball ends on the strings. This moves the ball end back into the body, silks etc now behind bridge saddles, Depends on what bridge the DMZ has, mine is BBOT fender style, others have Schaller (branded Kramer), have also seen Badass types fitted.
Mine does a bit despite the body weight. Largely but not totally cured by a wide grippy strap and forearm resting on upper bout cutout. Having stopped my SG bass neck diving by putting Hipshot lightweight tuners on it I am going to try some of the Schaller lightweight M4s. I might try a quick change of bridge to a Badass (borrowed from a bass I have from you) and see if that helps. I have also considered getting a replica body made with a longer upper horn.
Bonus feature of the DMZ4001 is the standard P size pickup. Plenty of readily fitting alternatives available if the DiMarzio is not to your taste.