Weird Idea Time...
I've got a current project, which needs a lot of DIP configuration switches, running on a 328P in a DIP package. At a fairly late stage I've discovered that I really need another bit. Every pin on the uC is already allocated. Changing to another chip is not an option.
I'm not using the ADC so AREF is unconnected. My thought was...
Select AREF as the ADC Vref
Switch the bandgap as the source to be measured to the ADC
If AREF is high, nominally 5V, then the ADC will return something around (1.1V/5V*1024) = 0x0D0
If AREF is low, nominally 0V, then I'd expected the ADC to return something around 0x3FF
...this feels so wrong that I hesitate to mention it. But sometimes needs must.
I'l try it later but will await the cry of 'are you mad' with interest.