I agree. If there are intermediate lamps, it's 1 pass instead of 3.
Yes, for a more even application of the white layer, it is worth putting down the first two sections of white paint and drying them after each layer.
Next, CMYK in line (you can dry it or not - depending on your target dot gain for each color).
If you're having trouble with the white ink sticking to the foil, try a different brand of white ink, adjust the ink's rheology with a reducer, or use a printing blanket with a different surface roughness. It's important to look at the exact appearance of the defect.
It's important not to expose the white too much UV radiation during intermediate drying. This will cause over-polymerization, and even at 38 Dyne or higher, the white will peel off onto the printing blanket of the following sections. Adhesion will be lost. The UV lamp intensity should be adjusted starting with a lower value based on your speed, foil, white, etc.