Hi Callum,
I’m currently investigating this issue but couldn’t reproduce this, would you mind providing your admin login credentials so I could directly test it?
What I did is, I enabled Under Construction and Woocommerce, then I set the home page as shop page in Admin > Settings > Reading (1st test), and or set the home page as shop page in Admin > Woocommerce > Settings > Products (2nd test), and both works as expected, it displays Under Construction page when logged out, and it display shop page when logged in without scrolling issues.
I can only replicate the issue if I set the custom Under Construction page as the shop page as suggested by Nabeel. Perhaps I could gather more information from your site about this issue.
Thanks!