We are talking about same plywood then.
There is difference between Stain and Paint. The cabinet grade might be covered with veneer wood, direct stain or paint would be OK just after brief 200 grit sanding.
As for the long stud, Homedepot should have 2x6x10' but hard to find straight ones. That is why some builders uses 2' segemented stud.
Can you post your design? Maybe you can use segemeted stud and disguised by paint or veneer.
The cabinet is strong from structural, not rely on one element such as the stud. The board, back board, shelf all contribute.
