Hi,
The buttons are supposed to be displayed at the end of the checkout, once the order is created, not before. Otherwise, the user could pay for his cart while his cart could potentially be changed after this, before the order is created.
The "payment" block is for the selection of payment methods, which you can configure by creating payment methods based on different payment plugins in System>Payment methods. The payment block mechanism has no visibility and no control on the buttons displayed by the PayPal Checkout plugin.
So, unfortunately, I don't see a way to do what you want.