That looks like a 7-degree rise stem. I'd consider three things:
- See if your LBS will loan you a 30-degree rise stem for you to try out for a ride. With a 100mm stem, that could raise your bars about 1.5 inches over your 7-degree stem (assuming that's a 100mm, as well). It looks like your current stem is already relatively short, so not sure what your options are there in terms of trying one size shorter.
- Switch to a modern, fatter-gripped bar if you're still on an older skinny handlebar. My Bianchi is a 2004 with a 25.4mm bar diameter (I think). When I got my Lynskey in 2019, I was surprised by how... girthy... the new 31.8mm diameter bars are. The additional surface area definitely helps distribute the weight across my palms, so I'm not complaining.
- What's your saddle angle at? Instead of lowering it, I would try tilting the nose of the saddle up a degree or two - this should have the effective of rotating your hips a bit so your weight is a bit more on your sit bones than on your wrists. This is especially noticeable if you've ever ridden a bike with a saddle that's very nose-down - all of your weight's on your upper body.
If the seatpost or stem alone help, then those are obviously the cheaper options - switching out bars, tape, and the labor involved is always gonna be a bit more annoying.