You could have the static homepage as just a normal page with the handpicked product block, and any other content. You could even sort of recreate the ‘shop’ page with latest products block.
Then have another page designated as your ‘shop’ page. You can choose whether or not to link to this in your menus.
The main thing to be aware of is that the designated ‘shop’ page is not designed to contain any manually added content, only the automatic output of the products.