Furniture in the Raw is the place that would build it. They do good work and use all solid wood with no MDF or particle board but in some ways it's like lincoln logs because they have a bunch of pieces that are of a known size and you have to take those sizes into account.
For example, the 'stiles' (that's what they call them) are the vertical support pieces and they are always 1.5" wide. The fixed shelves are always .75" thick, the base is always 3.5" tall, the top shelf is always 2" thick, the crown molding adds .75" on each side, etc. When I look at all the designs from Salamander, StudioCraft, BDI, and others I see stands that meet my width requirement and have other features like sliding doors and removeable back panels but it is because they don't have the same restrictions - their walls are thinner or the stiles are thinner, the base is just feet, etc.
Without increasing the dimensions my only choice for doors are normal doors with inside hinges. I'd love to have the kind that slide left or right or pocket doors that can be recessed into the unit but they would push out the dimensions further. Same deal with a removeable back panel but I can ask if that is an option.