If you curl your finger and push the shifter with your fingertip (instead of pushing sideways) that might help.
I never had those issues when I used down-tube shifters, but I did stick a finger into the front tire a couple times.
I also had bikes with bar-end shifters. I always liked those.
I have pain in the base of the thumb, mostly on the left hand. Something to do with holding handlebars for almost 40 years.