Save yourself a lot of stress and greatly improve the depth of coverage overall, by using oil or water based primers tinted to as close to the top coats colours as you can.
(Not aware of anyone tinting Zinsser BIN, but correct me if I’m wrong)
Update old post Holman Paints offer tinting of shellac primers.
Your paint supplier should be able to oblige, running the primer through the tinting and shaking machines for you. Depending on sheen, it may be an identical match, or it may be close. Having it tinted in the store is much more efficient than tinting your own, but if needs must, especially with stronger colours, it will still be a time saver tinting and mixing 2.5 litres of white primer, to somewhere close to the final colour, by hand.