Cabinet recommendation

You might consider having one of the advertisers of custom racks make you one, assuming you can't find one already made.

Any recos?

Timbernation can build you anything you want.  Very high quality workmanship.  

Try Googling credenza, sideboard, record storage (or something like that).

Example:

https://www.departmentchicago.com/product-page/60-record-cabinet

DeKay

Thanks Dekay! Yeah that cabinet you linked is the closest thing I’ve found to what I’m looking for - unfortunately they cannot make drawers in the size I need. 
Any other reccos?

I missed the CD storage part.

I store CD's (on end) in the shallow drawers of an old Tansu cabinet (holds 1200+).

Perhaps consider storing the CD's/LP's in separate units?

Many use Ikea units for LP storage as they come in various sizes/configurations, and they are cheap.

A shallow drawer credenza/sideboard could hold the CD's with the electronics on top.

Six months ago I would have suggested hitting the local thrifts/used furniture shops for a REAL piece of vintage furniture that would work, but realize that doing so is no longer feasible for some time to come.

Custom work here/Los Angeles costs a fortune (think they charge $135/hour for the glue to cure).

DeKay