Hi, I'm new to the forum, but wanted to put my two cents in on this.
Generally speaking, the only time I think it would be worth the money to go with an Apple or Euro Ply is if you are joining the ends or your fiinished product will have exposed edges like in the drawer pictures above, which are beautiful by the way. I will say that I am biased against Chinese plywood of any type,( I have worked in west coast plywood manufacturing for 20 years) and have heard too many horror stories to count, but if you are getting true Baltic Birch from Russia or Poland, the quality should be good. The Chinese are masters of misrepresenting product, i.e. marketing a product as Baltic Birch when it really isnt, and the big box stores buy a lot of low qualty Chinese product to keep their price points low. If you want to make sure to get true Baltic Birch core plywood, or any other plywood for that matter, that won't delam when you cut it, I would take Dave's advice above and find product that is produced in either the U.S. or Canada. The price will be higher but you should have much better luck as to the quality of the panel, and a lot less waste.