Been doing this for years the same way. I'm a body/paint guy but anyone can do this.
Small 5 gallon bucket with lid. Cut 9" hole in bottom side of bucket. Tip upside down.
Your chunk should fit nicely and with lid on will hold any residue of gear oil.
Degrease #1. Prep with carb cleaner or reducer or thinner, 3 times, and do again.
Use plastic small bristle brush getting in nooks and crannies. Rinse thoroughly.
Repeat this step, several times.
Dry off and steel wool with 00 or similar in all areas nooks/crannies.

I use rust inhibiter as a primer.(in photos)
2 light coats that's it, let dry 30 minutes.
I use caliper satin paint spray can. tolerates heat.
Again, 2-3 light coats to cover,The less material the better.
When satisfied with coverage, done.
less than 2hours time. Sit overnite ready to install.

I did my chunk in 67 Barracuda in 1995, still the same as when I painted it!

Good luck and will save anyone alot of $


Dave