We want to avoid staining as this will result in coloring in the open grain. Apply it to the lighter staves and mouldings to make them blend better with the darker. A sap stain is made fairly easily and some manufactures even offer one for use with their system. If you want to make your own, here is a starting point. This will typically be a combination of raw umber, red, yellow, and brown.
White oak is the problem here.
Ash bleaches much more evenly, no dark grains like white oak. After bleaching ash, tone in color desired with a methanol dye mixture. Or if just white oak, bleach only the dark grain and tone to match. Ilva's urethane is fine to use over methanol dyes. The product you use is very good.