I have had similar issues (due to a long term left wrist injury (think 11 ops over 15 years to repair it)).
What usually works better for me is to shorten the stem and raise it slightly, so there is less pressure on your wrists and more on your ass. Add ergon grips GP1's and
SJSC's own bar ends, along with full finger gloves. I avoided the short finger ones becuase my hand sizing is smack bang in between the sizes - get the ones that fit my palms and they are not noticeably too tight around the fingers until you start to ride and your fingers swell slightly - result finger ends going numb. Get the next size up and my hands move around way too much. for some reason, long fingered gloves don't give me as many issues.
I also changed the bars from flat bars to
Thorns Comfort bars, only on my touring bike (I would have done on my mtb, but sold it to help pay for the touring bike). They are angled better for wrists and comfort (think they are designed by a physio) for touring and for me they made a considerable difference. My OH stayed with straight bars on our touring bike.
The difference all that made - well 2 weeks touring on a MTB left me with a numb left hand for about 6 months. 12 months touring on my touring bike using the same gloves, same grips and same raised & shortened stem has left no issues (except wearing out numerous pairs of gloves!).
Regretfully it is one of these try it out and see things. Start with the stem & grips if you know your gloves are OK. They are easy (if fiddley to replace). The SJSC bar ends, add an extra 'pad area' for the lower palm, leaving a gap between the Ergon GP1 grip and the SJSC bar end which is where I naturally found my hands - great because that is exactly where the nerves that cause my issue happen to be. I'll try to get a photo to make it clearer....