Can you substitute a beveled washer in a faucet for a flat one?”
Beveled washers are designed to fit well into a beveled valve or surface. The bevel will be that much less surface area to hold the water pressure back. And I don’t think it will ease the tension necessary to stop all drips. The tension in the valve core means that the water ways in the core are worn, and wider than they use to be. The core must be turned farther than normal to cut off the flow. The farther you turn, the more you compress the washer and tension builds. If you replace the core, it should not need to be turned so far. It could also be that the faucet is worn, but this is less likely. Replacing the entire faucet is a big job. I would start with the core. I don’t think the beveled washer will do it, but it is cheap to find out.