Not sure if this was already posted already (A lot to read). Maybe looking at an interface of some kind where the user may apply it to a curved surface.
If what you are holding in hand is to be used in the design then it depends on what that soic-8 can do. Am thinking a touch controller that reports to a master via i2c or spi. The coin cells can power the entire system (if it does not have any power hungry parts). The problem is that we do not know what the (round looking part) is.
Another idea could be a control system for (anything) that can be fixed to the inside of a cap (hat). As i said it depends.
I we can suggest an actual design then one could look at small data terminal (something to get people interested in doing more than just buttons and switched)., one that has a sort of hinge. you could use one of the displays that you sell and make the keypad from a pcb similar to the simon, or even they could make a flex keypad that can be placed on a plastic surface (the inner side of the clam shell.
Something entry level (no need to be complex-ed) but something that does a bit more than the occasional arduino. You could even power it by a Pi so you get some real punch out of it and maybe use one of the psp lcd’s (Can the flex wires handle that high bandwidth?) Maybe you could use a mall breakout board on top of the section that connects to the LCD so you dont have to do any fine pith soldering on it and the actual spots on the flex could be say (2mm apart each). something like that.