Okay to drywall over siding?
Are you getting rid of that sliding door? Not sure how your going to attach casing to it.
If you used 1/4 you would not have such a big problum trimming out the door, and you could kill the power to the outlet then remove the screws holding the in place and twist it from to to bottom to get it out of the way, install the sheet rock then reinstall the outlet without having to use spacers.
When trimming out the door I would assemble it laying down and use Tite Bond II and nails in both directions then you leave the sheetrock back far enough that the casing will have room to flex and fit flush.