John B wrote:

How would you finish the inside of the dado to prevent the particle board
from crumbling, and make it look right?

Don't use particle board, use Valchromat instead. It's a high resin
content pre-coloured MDF. Looks as good on a cut edge as it does on a
sheet. Wax polishes well and also resists bathroom levels of moisture.

http://codesmiths.com/shed/furniture/cabinets/swarf/