Len - there are multiple reasons colorings blotch. Incompatible products, incorrect preparation, and the worst - contamination.
Contamination can come from anywhere. It could be on the ply when you buy it, it could be something in your finish, or it could be as simple as using a rag from the rag bag instead of a clean rag. The love of my life put softener in every load, even those destined for the rag bag, so they are loaded with silicones and other agents.
If you are having problems with "terrible" blotching after your sealer, there is a easy way to test that will give a good idea (not foolproof) of contamination. Try this to see if you are having a compatibility or contamination problem.
Put some colorant in a clean spay bottle. You can get these at the $1 store, and it will be worth a buck to see if this is the problem.
Spray it on a couple of the LIGHT areas, not the dark. If the colorant beads up on the surface into a million little beads, you have a problem. If it lays flat and simply shrinks at the edges, you are probably fine.
If you have a contamination problem, start over. Even if you spray a toned finish on a contaminated surface and it looks fine when finished, it may not hold up. Finishes today are so good they will fool you for a while by looking great. But if they don't adhere properly, there will be problems later.
Birch ply in particular can be tough to get right.
The biggest alarm bell you sounded though was the fact that you were using a water based dye on top of shellac. Depending on how you applied your shellac, and how much you sanded, etc., your shellac will have different levels of porosity and water repellance. Think about this; if you set a sweating glass of water on a table for a few of minutes, the water won't penetrate as it has some water repelling properties.
This could easily be the problems with your dye. And if you are apply the dye with a rag, brush, pad, or anything else by hand, the dye will be sucked out of the applicator by the more porous areas of the ply. You don't stand a chance at an even coloration.
If it were me, I would recreate exactly what I now have on a few pieces of scrap. Then i would work on a solution, whether it be sanding and recoloring, toning, changing finishes, etc. Just applying a mask over the existing "terrible blotching" may mitigate the poor appearance, but then you will be making excuses for your work any time you show it off.
Don't think applying a toner is that easy, either. A tiny bit of color applied well is in fact pretty easy. But if you are applying enough color in a finish to cover up problems, you are essentially adding a thinned, colored paint. Again, try this on your prepared, blotchy scraps and see what you think before going to your project.
Robert