The problem with my '02 Buick Regal started with a pronounced hesitation and "miss" on acceleration and it set a "multiple misfire" code. I always start electric diagnosis with a battery check, and yes, the battery had gone bad. Tested alternator--it was good. I replaced the battery, started the car and over 2-3 minutes the running deteriorated to a stall and then no start condition. Had the ignition control module tested--it was bad. Ohmed the coils and got consistent, but high resistance on all three, so I replaced the module and 3 coils. Car starts and runs, but still misses. Next morning the new battery is not only completely discharged, it has gone bad. I exchanged the battery and took the alternator to a shop for testing. Alternator tests as good. Install battery, car starts and runs, still has the miss. Next morning, second new battery is discharged and has gone bad. There is no evident short circuit or damage to the cables. Am I just having bad luck with batteries, or is there some other explanation for this battery killing phenom? I just metered a 0.9 amp load on the battery with the ignition "off". This seems really high. What could pull that much current? I don't think any interior lights are on...

That is absurdly high. Your next step would be to start yanking fuses and checking battery cables to make sure there is no shorting to ground. When you yank fuses, pay attention to the load. It should drop substantially once you remove the fuse from the affected circuit. Pull them one at a time so you don't get mixed around.