This was very helpful! Thank you!

Now for a bonus question: How about the option to use the code on https://jetpack.me/2013/10/15/ever-accidentally-publicize-a-post-that-you-didnt/

add_filter( 'publicize_checkbox_default', '__return_false' );

to apply to just woocommerce product posts? I.e. all other posts are auto-selected, but product posts have the publicize option, but aren't auto-checked.

Any thoughts?