Op did mention that that it's impossible to get the rack out because they installed the doors after the rolled the rack cabinet in

It's obviously not impossible, just need to take it apart.

Or pry the door frame apart and tap it back in place after rolling the rack out.

Worth a mention as many door frames are easier to remove than a number of people might suspect .. fewer pieces to disassemble than many {object}'s and not an uncommon hack when moving furniture.

Removing door frames is easy. Putting it back together without looking like crap is the hard part.

Repeat after me: caulk and paint make it what it ain't

For the one I have that would be irreversible. You‘d have to cut it up.