I think that rusomon's answer may be as close as you'll get. Not only were there a bunch of companies offering furniture grade speaker cabinets to put your components in, there were plenty of pieces of furniture that got repurposed into speaker cabinets, so tracking the exact make may be a big challenge unless you are lucky and someone recognizes them.
When AR came out with acoustic suspension speakers in the late 50s, they were unusual in being offered only as a complete system. Normally drivers and cabinets were separate purchases, though obviously you could buy combinations premade. Bozak was famous for producing enclosures that could have more and more drivers put in as the budget permitted, so the driver combo, not the enclosure determined which model you had.
Were I you, I'm move the components to a different and larger set of cabinets.