that is a really good idea. i am weirdly claustrophobic because of PTSD from being assaulted and choked for three years.
i was wearing a scarf around my mouth when it all first played out. it was nothing short of feeling like i am being choked and don't have any oxygen terror. it took me loosening the scarf, wearing it like that for a few times to be able to tighten it.
i still have panic attacks with a mask on sometimes and have to get away from the area to get fresh air.
it sucks but i think the suggestions also of wearing something loosely constructed to hide your mouth is worth a shot. try that around the house for a few days to see if it helps.
all the best to you. that suffocating feeling is awful.