I just keep all my 2 and 4oz bottles in a box in my vape cabinet. I consider them to be refills. However, the stack on cases I have will allow to lay down a 4oz bottle and still close.
I have two similar to these. I don't think my cups pull out though.
https://www.lowes.com/pd/Stack-On-Deep-Cup-Organizer/50329811
They look similar to the ones at HF. And HF has the Plano style boxes for $3.99. I have thought about this route and a wall mounted nail polish rack in metal.