Guess I was lucky... The first time I ever needed Baltic Birch I searched all kinds of places on the net. Finally while I was at my local hardware/lumberyard for something else I asked a guy at the counter if they had any kind of ''premium plywood'' (they mostly sell OSB and subfloor ply). The guy answered follow me, we've got something in the back. And there it was... Very nice quality baltic birch, one side free of any voids, always in stock from 1/8 to 1 inch in 1/8 increments. I felt like the guy who spends 4 hours troubleshooting why his car won't start, before realizing he's low on gas or he forgot the headlamps. I was already prepared to drive several hours to go get my plywood in larger yards in larger cities... All I had to do was drive to the next corner.
In the case you didn't do this recently, I'd suggest to first forget about exotic plywood distributors and such places, keep these as last resort. First do a methodic list of small, independant lumberyards. Call them and make sure you talk to someone who knows his stuff. If you can, try to talk to the guy that actually works in the yard and/or places the orders to lumber suppliers. Nothing more frustrating than to be answered no when the product you want is actually in alley 7 next to the chistmas decorations...
In big box stores, they have what sells, and more often than not what is available is what the franchise headquarters think will sell. In independant stores, depending on who runs the place and who the customers are, the things you see in stock may vary a lot. In small places the folks will often even offer you to find what you're looking for and order it for you.