Designing an ultra-thin battery holder (CR2016)
A lot of clips on the market support more than one battery thickness. Try looking at ones that only support 2016 (and maybe 2012 size as well). For example, I was able to find a 2016-only clip from Digikey that is 2.16mm thick (nominal).



That extra mm on a 2016 holder is there primarily for the spring contacts that hold it together. You could take it away completely, and use a 2016 with SMT tabs attached. Depending on your device needs, you could just solder it down, and you'd be good. From Digikey, I found a 2016 cell with leads on it that is 1.87 mm thick.



If you wanted to make it removable, I could imagine some clip or screw holding down each lead flush to the PCB, and then you could have a bit more vertical space to get the spring/screw in there.

Alternatively, if you want to use a plain 2016 and since you said you were game for some fabrication, you could try making the the traditional metal style clip without a spring. That should save a fraction of a mm. To get good contact, you may need to put a piece of shim metal between the battery and the clip, or have some sort of ridge built into the clip to provide pressure on the battery. The caveat here is that you might not be saving much thickness and you may be introducing a source of unreliability.