There is nothing inherent in the way that the screens are constructed that could cause a failure as described solely due to altitude.
The battery packs are a different matter since they are formed of sheets of materials and an electrolyte packed into a relatively flexible outer package.
The battery pack can and does swell as atmospheric pressure is reduced or due to temperature increases. A bit of extra space is designed within the casing of Lithium ion battery powered devices to cope with this expansion. That is why the battery packs are firmly glued inside most devices to stop them moving and to provide an efficient thermal path for cooling.
I have personally experienced the deterioration process twice and observed the screen discolouration effects, a screen unexpectedly shattering in one case and the screen being lifted from the casing in another. Both times were due to an aged battery swelling and applying pressure to the back of the screen.
The process occurs over a period of perhaps six weeks from the point where the battery pack starts to swell and cause the slightly darker blotch along or across the display screen. Higher temperatures seem to speed up the process slightly, but have a slight remedial effect in that they act to soften the glue holding the screen in place. So the screen may lift and separate from the casing in a controlled manner, rather than shattering from increased internal stress applied by the battery.
Low atmospheric pressure, i.e. altitudes above 10,000 feet (3,000 metres) results in decreased cooling efficiency of all electronic components. However in the case of a deteriorating battery pack that has begun to gas excessively, the gas trapped in the packaging will undoubtably expand and cause the battery casing materials to swell. This is the underlying root cause of the failure and the reason behind the advice not to operate Lithium ion powered devices with internal battery packs above a certain altitude.
The reality is that a new device with a fresh battery would probably operate just fine up to perhaps 30,000 feet, while a device that had been heavily used over two or three years could be expected to fail at less than half that altitude.
One possible solution would be to remove the internal Lithium ion battery packs and operate the device from external power sources only. Portability could be maintained by using an external battery pack made up of good quality 18650 metal cased batteries as these are more robust with regards to swelling due to altitude changes. Replacing the external battery pack every year would be a relatively cheap way of ensuring safety and optimum battery performance.
Operating directly from the aircraft power supply is possible using a suitable voltage converter, but not recommended as aircraft power can be electrically noisy, or fail unexpectedly. One less thing to worry about in an emergency if the nav screen information remains visible.