OP: I was thinking of pulling the engine to work on it easier, paint it, etc. BUT, I have never done that before.
If you compile the answers so far you have the Lions share of 'How' to go about making the job easiest.
Is this a shade tree job or do you have a work space?
What sort of time parameters do you have in mind?
You don't need many tools (You Do have tools don't you?)to get to the bare engine ready for paint but a box of zip lock bags and some perm. markers will save your sanity down the roads IF your disciplined enough to use them....
I'd avoid the lacquer thinner as it leaves a residue and just evaporates to fast to help. Kerosene is cheaper anyway.
I found after the flexible putty knife, a straight line from the hot water tank to my pressure washer was the easiest and fastest way to go.
Then the foamy stuff if needed, otherwise I like a strong solution of Simple Green or Purple whatever, and (the important one) Dawn original in a weed sprayer. (again mixed with HOT water)
Spray, Rinse, Repeat.