I seem to be able to develop tolerance for this. I've had this happen to my right hand out of nothing. I rarely switch my hand position on the road bike, so I am trying to do that more, too.
I cannot withstand *any* padding in my gloves. In fact, I have to search far and wide to find unpadded gloves. I get extreme squeezing feeling and pain from just a tiny amount of padding, so that is out. Trek stopped making the gloves I had worn for years, so I finally found some from Giro.
2015 Trek Silque SSL
Specialized Oura
2011 Guru Praemio
Specialized Oura
2017 Specialized Ariel Sport