I'm not sure what sort of STI levers you have that require the lever to be pushed outwards. I only know ones where both levers push inwards, but clearly there are various types I'm not familiar with. In terms of twist grips, I had a SRAM twistgrip for several years on a flat-barred bike and it had two problems: when new it was crisp and easy to use but over time, the internal gubbins wore away and it became rather imprecise in action; and more significantly for you, it did put load on the joint of the thumb and palm. I'd have thought down-tube levers, or maybe bar ends, would be better in your case. But it sounds worth experimenting with different shifting systems to find what works for you.
I was thinking the other night "got that wrong!" but the STI ones that I have (and that even though they're old work very sweetly) have the brake lever that moves to pull the cable and a parallel lever underneath (or inside if you like) that releases it. I think it must be the inside lever that plays havoc with my thumb but since I am not using them (although the levers are still on the 992, just operating the brakes!) and the bike is on the rack for the winter I am not going to go out and check it.
3kms with the Alfin bike tonight riding back from dropping off a company car and I felt every minute of it with the shifters. This is on flat bars so the only other option to me looks to be twistgrip. They're cheap as well.
Both the dérailleur drop bar bikes are on downtube shifters, indexed on the Gitane and friction on the 992. As Brucey has remarked, modern sprocket profiles and shifting technology make dt levers a joy compared to what they were in my youth (but indexed is the top, even with my cheap Sunrace levers).