If you're using alcohol-based paste, of course it's going to sting. That's why there's no-sting paste.
If you're using alcohol-based wipes, of course it's going to sting. Anything with alcohol, especially trapped underneath, is going to constantly sting.
A ring is flat on the bottom, so it doesn't fill gaps or dips as well as paste.
So what I'm seeing here is your skin is tearing, and output is just getting under the ring and causing constant pain.
You apply a thin coat of paste around the stoma to fill wounds, etc., and to make sure the paste sticks to the skin.
Then apply a bit more on top to marry to the wafer. The paste needs to be about as wide as a ring.
You use a coffee stir stick or something to handle the paste so it's not on your hands. You wipe it off the stick using toilet paper by pinching and pulling it off.
Don't touch the paste with your fingers.
You're using other types of products under your adhesive, and they are not designed to be bonded with it if you're not allowing these other products to breathe, being trapped underneath.
Some liquid wound stuff contains alcohol, which can burn.
The skin will heal just fine under there on its own, once it's sufficiently protected from stoma output.
To remove old paste from the skin around the stoma, you first use another coffee stir stick or something flat and sideways scrape it off. Not using your fingernails as that can dig into the skin and damage it. If you have leftover sticky residue, you use the abrasive side of a new dish sponge and sideways stroke scrub it off. It just transfers inside the sponge.