Can I avoid re-customizing my theme from scratch after an update?
You can avoid re-uploading and applying the settings, but there are a few steps involved !
You can copy over the content of the file
config/settings_data.json from the current to the new theme. That file contains all the values to which your current theme settings have been set.
You'd also need to copy over your assets (logo, slides, promos, etc) from one theme's assets folder to the other, requiring that you download both themes, your current one and the new, and copy over files using your operating system file manager application (on a similar topic, read this).
If you made any edits to the style.liquid.css file you will need to copy those over as well.
One last concern but not the least: uninstall and re-install all of your Shopify applications that add code to the theme layer.