I would recommend changing your hand position from the hoods to the bar tops to relieve the pressure on your shoulder. Also either double wrap the bar tops or use your insulation strategy. Doing more core strengthening exercises will also reduce the amount of pressure on your shoulder leaning forward. In addition, try raising your stack height.
The ultimate solution would be a shoulder replacement, but I know that is a big ask especially if it doesn’t bother you otherwise.
Best of luck.
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Road 🚴🏾♂️ & Mountain 🚵🏾♂️