Not familiar with the 5.3, but I recently had a misfire on cyl#4 on my 5.7L Hemi... only on hard throttle, tho...

swapped coil between #2 and #4, swapped injectors between #4 & #6... but tapped the injectors upside down on a paper towel while they were out- #4 had some crap come out (there's a pre-filter/screen in each injector)... was going to see if the problem moved or stuck with cyl#4... but instead it went away...

flow was too low with the crap that was in the screen is my guess... runs good now, no codes- 207k miles

whenever you have misfires, there are the 3 things needed for reliable ignition- fuel (in the proper ratio), spark, and compression...
Though I have heard of some engines that will throw general misfire codes when the crank sensor is failing... (doesn't give reliable data to the computer)