Have you put a DC ammeter in-line with the iginition sense line to check the amperage you're using when everything's powered on? So long as you're less than the fuse that controls the line you should be OK. You could also check for voltage sag when things are turned on (indicating a resistance upstream or in the wiring). Low voltage may be a bigger problem than popping fuses, depending on your car's wiring.
Of course I'm assuming you have also got the Sony head unit wired to permanent power as well as the ignition sense line, no (ie the ignition sense line is only used to tell the Sony when the car is on - not used to drive its amplifiers)?
Of course a relay would work as well, but they do take up space, which may be at a premium inside your dash. I'd check to make sure you really need one. I used one to cure the old power off thump issue (before the diodes on the empeg harness).
HTH.
-Zeke
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