Your situation with your hands seems very similar to what I deal with. I have had real trouble keeping my hands warm for my whole life. The circulation in my hands starts shutting down for the slightest excuse when they are exposed to cold, and in actual cold weather (and now I’m not talking about paddling), I have limited ability to keep my hands warm even inside very good mittens. I recall several times when I was a kid, during winter, when I’d tell a friend that my hands were painfully numb and I couldn’t get them to warm up, and the friend would offer to trade mittens for a little while. When I first put their mittens on, it always felt like there had been a little furnace running in there. The hands of normal people stay warm and radiate heat so the inside of their mittens get toasty. My hands only get that hot feeling inside good mittens during extended strenuous activity like hiking in difficult terrain (paddling is not that strenuous in comparison), though in very cold weather, even strenuous activity may not be enough to make my hands warm.
I only mention all that stuff to make a particular point here. I saw a bunch of recommendations here, many years ago during the older days this message board, about various neoprene gloves and mitts which were made either for paddling or for diving. Each person who had a favorite would say “these things will keep you warm”. I’m here to tell you that for a person for whom the circulation in their hands shuts down in the cold (and I’m not the only person who has that problem), ALL of those special gloves and mitts for water activities are USELESS! Don’t be disappointed if recommendations for dive gloves and the latest-greatest paddling gloves and mitts turn out to be at least as bad as wearing no gloves at all, and possibly worse than that. That’s how it is for some of us.
I learned by accident that plain old wool mittens or gloves, with a windproof shell over them, work extremely well in my case. Long ago, I went on an early-spring river trip. I knew it would be raining for much of the day, and I knew that the temperature wasn’t going to be any warmer than the mid-40s, so I bought the best, “warmest” paddling mitts that the local shop carried. I already had a standard pair of neoprene paddling gloves which I had hardly used (but already knew they probably wouldn’t work). Both the gloves and the super-fancy mitts turned out to be worse than useless, conducting heat away from my hands seemingly even faster than when my hands were exposed directly to the air and rain (that may not have been true, but it sure felt that way since there seemed to be ZERO insulating capability, and when taking them off I did NOT feel any increased exposure to the cold). I also had a pair of light wool gloves - simply knitted from yarn - and a pair of wind-shell mitts (this was not paddling gear, but just something I brought along to increase my options). I put those on, and within 10 minutes my hands were soaking wet from the rain, BUT, they were rapidly getting warmer! I wore that combination for the rest of the day. The wool gloves and wind-shell mitts were literally soaked all day long, so much so that I could sling streams of water out of them by swinging my arms, but at no point during the rest of the day were my hands even the slightest bit cold, and for me, in such weather conditions, that’s quite an accomplishment.
I’ve totally given up on modern materials for gloves or mitts for paddling. For me, those don’t work in the slightest. In dry conditions, good winter mittens are better in my case, and wool as the main insulating layer is the ONLY thing I will consider if my hands are going to be soaking wet. I’m not telling you to just get some wool gloves and wind-shell mitts (I know that some people just won’t like this idea, though it might turn out to be what works best. OR, wool gloves might be just the thing to wear inside of pogies). Anyway, from one cold-hands person to another, I advise you to face the fact that people who can successfully keep their hands warm can never understand what you are up against, and they will never understand how useless their advice is when applied to others who naturally have difficulty keeping their hands warm. You will have to consider options that normal people don’t need. Lucky for you, it sounds like your situation with the circulation in your hands shutting down in the cold is not quite as bad as what I deal with. But I get it.
One more comment about wool. I have similar issues with my feet as I do with my hands, so I always wear very good footwear in winter. I wear “shoe-packs” with wool felt liners plus a combination of a synthetic liner sock and two layers of wool socks. A number of times over the years I have accidentally stepped into water deeper than the top of one boot on a very cold winter day, and not a single time did the soaking-wet conditions that followed have any noticeable effect on keeping that foot warm. In fact, one foot has a slight tendency to get cold more easily than the other, and if that was the foot that remained dry, that foot would still get cold sooner than the foot that was soaking wet, just as would be the case if both feet were dry. Wool is amazing. I love some of the modern synthetics, but in my opinion, no modern synthetic material even comes close to wool in its ability to keep insulating really well when wet.