+1..what Mike said.
If it were me..I'd put the energy/time into a good paint job. It'll be tough to get a merlot(dark) stain off well enough to reapply a different stain and have it look like anything**. Birch itself tends to blotch badly..as the merlot finish may indicate. Bleaching it after removing the topcoat will raise the grain and open it up..leading to worse blotching yet when you refinish. All this work will require some sanding. You'll be working on a veneer, so be careful. Sanding the open field areas can be easy with an orbital sander, but getting the same quality of sanding / surface removal / surface in the corners where planes meet.. very time consuming.
**If you want to go this route: remove the drivers, strip the topcoat with a stripper, sand a little to make sure all of the topcoat is completely removed, try bleaching it in a couple obscure sections to see what happens..bleach as Mike said or oxalic acid wood bleach(woodworking store), neutralize it, dry, sand to 120-150 grit, use Transtint wood dye using ethanol as a carrier(not water)..a darker tone will tend to cover faults better than a lighter stain. I'd spray it with 1# shellac after the dye, and topcoat as desired.
Consider that baltic birch, even when new and stained/topcoated, isn't much to look at as birch has little grain that's very interesting. It looks best when you make the finish-quality the key point rather than the 'beauty' of the wood. In cases like this, the stain just gives a nice tone under a better looking topcoat.
And then you still have the edges to consider..or at least how they appear. They too look best grain-filled with a great topcoat to highlight the wood-stripes.
If the restain doesn't work, I'd still remove the drivers, fill the edges to eliminate the roughness, (spray) paint(not rattle-can), and topcoat.