I have an app which does exactly this - upload and store PDF documents of substantial size.
To handle the upload timeout issue, I use a client writable view (https://anvil.works/docs/data-tables/data-security#views).
My media uploader loads the file into this view and I then call a server function to write it from that view into my real table (and then delete from the view, all within a transaction).
Hope that helps!