ok, how wide is the bottom of the box is my next question. IF it's just he 6", you can turn it end over end on your tablesaw and slice away teh 15/32 or whatever to get your quarter inch. You can use the planer, I just don't advice it, it's loud and can be tough on some blades. Not to mention if it's a chinese product you never know what you're gonna find in there….
One of the main reasons I love Lacquer is it's forgiving nature. It can fill in wide grain very easily, you just use proper sand papers, not steel wool, and unless you get wooddust in the project while sanding, you just recoat, the lacquer remelts filling in the voids. It's a beautiful thing really. And I know alot of hobbyists tell you to wipe it down with mineral spirits and tack cloths and do all kinds of silly things, but honestly I just sit back and shake my head when I see that.
Now with virtually every other form of finish, you'd best wipe it down, blow it off tack cloth it, jump up and down 3 times while touching your nose and so on…