I'm not sure about board availability. Yuneec GB or Germany might be a good contact. An entire used controller might be almost as cheap as a new board.
Both of those pots go through the same connector bundle from the button board to the main controller board. It might be worth unplugging the connector on both ends a couple of times to see if there is corrosion in the connectors.
The Factory reset on an ST16S will erase the main flight APP. You will need a copy of the APP prior to the reset and will need to re-install it after the reset. A screenshot of your controller versions page will help us provide you with the correct version of the APP. The reset itself is in the Settings menu.
An update attempt might not be a good idea yet. Failed updates are a common cause of all kinds of controller mischief, and your controller is apparently already having difficulties. If an update looks like it is necessary, it can be done using SD cards instead of the factory OTA system.
www.dropbox.com
The screenshot of your controller versions page will help us know what versions you have installed.