Gunkote will adhere well to parkerizing. Just be sure to thoroughly degrease it before you spray. Apply thin coats with gunkote and bake per the instructions. I like to warm the parts before spraying.
Examine the parts immediately after they finish baking. You can touch up places you missed as long as you haven't handled them. Then re-bake the part per the directions.
8 ounces of gunkote should do all the jobs you listed.
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