Thank you all for the great ideas. I ended up ordering a 3 section frit tray from Mountain Glass Arts. Here's a picture:
I think it'll be a good investment - it looks to be perfectly sized for blown ornaments and tumblers. I tried a shallow stainless steel tray we already had, and I immediately understood why it needs to be shallow and why the gravy boat might not always work. Anyhoo, just wanted to thank you all for the great suggestions!