It is impossible to tell you what you need to do without actually knowing or seeing you on the bike. But in general all the above are things to think about that may help but also they are like shots in the dark at your problem with the exception of getting properly fitted as a starting point. It is also possible to do your own fitting with some understanding of the process and also knowing your own abilities. The self-fitting with some understanding of what you want to accomplish is ok but you can see from just a few posts everyone has different ideas about what posture they like. Upright is ok but you will be fighting the wind and on longer rides the pain can move from the support of the hands to the support of the back side. Upright posture also IMO doesn’t involve all the muscle the same as a more aero position will.
The one thing mentioned above I wouldn’t recommend is moving the saddle forward to reduce reach and making a more upright posture I an attempt to take weight off the hands. I have found doing that can actually put more weight on the arms and hands and here is why. The first thing I do when I try and fit myself on a new bike is get the saddle height correct for the amount of leg extension I want. The second thing is to adjust the saddle front to back regardless where the bars fall at. The crank doesn’t move and you need the saddle in the place where when seated you are far enough back that you can have balance using your core muscles reacting against the push of your legs. Much of your upper body weight that’s now on your arms can be held up with your abs and counterbalanced by your butt moving back. For an experiment stand with your heals to a wall and a chair in front of you to use like handlebars start leaning forward to put your hands on the chair. You will want to fall forward because your upper body weight can’t be counterbalanced with your but moving back. Now move out from the wall and try it and its natural to shift the weight back at the same time you bend forward and you won’t even need the chair for support. I try and get that same feeling on the bike. I will attach a photo I found on line that pointed out the posture to me.
As far as padded grips or padding bars I have done both. If you have wrapped bars there are gel pads you can put under the wrap I sometimes use some of the old tape under some areas where I want a little more pad. The grips that have the paddle on them are nice also. Having more than one hand position helps the most and you can get that on some bikes with adding bar ends that will also take a mountain bike grip if you like. Trekking bars also give lots of hand locations and work well. The best tip I have found for numb hands is the spot on the hand that you put the pressure on. It has to do with blood flow and nerves and such. But the pad opposite the thumb pad on the outside of the hand is where I try and put the weight to avoid numbness, that and keeping the wrist angle both ways about in the middle of the range of motion. Straight bars for me are the worst and I know many like riding them and have no problems.
If you get your saddle height and position correct and you are faced with the wrong reach you have to then fix that with stem and bars. Likewise bar height is important and that can be fixed with stem and bars. IMHO no one would solve bars to low by lowering the saddle and by the same token you shouldn’t fix reach by moving the saddle forward.
I added some lines to the photo of each rider showing where the shoulders are related to the crank and the stem. You can be the judge of what looks best.