That’s how we make(made) them, except for the gloves.
We used a spoon to get the eggs in and out of the dye.
We also mostly used food color and no drawing on the egg with a pencil first. Just do it free hand.
For polishing, we’d use an old pie tin and a warm cloth, like old undershirts. We’d put the pan on the stove on low, rub the cloth in the pan to heat it up, and then buff the wax off.
I did end up deciding to spray mine, too, to keep the color from smudging if it got wet.
Also, don’t handle the egg any more than needed. Even the oils from your hands can cause the dyes to not take very well. It makes them blotchy.