While researching LP storage cabinets I found Jenn Atocha of Atocha Design, in New York.
Atocha cabinets are extremely well made and are very heavy. I offer up two suggestions that you might consider inquiring about before you finalize your order. First, see if you can get Jenn to countersink the screws holding the drawer fascias and pulls in place. The drawer's fascia retention screws are broad and flat-headed but still sit a bit proud of the inside surface of the drawer. The drawer pull retention screws OTOH are round headed and stick out about 1/8" off the inner drawer surface. You run the risk of scarring the cover of the first LP in the drawer if you overfill the drawer. These round head drawer pull retention screws should be flat-headed and countersunk to prevent damage to your album covers.
The second recommendation would be to see if Jenn could increase the depth of the drawers by 1-1-1/2". The current drawers are a little over 13.5" deep and barely accommodate the top edge of a 13x13 LP jacket with protective mylar cover. If you happen to top load 5-mil protective covers or want to use tabbed dividers there is simply not enough clearance to allow the drawer to close.