Rather than override the success.phtml file, add the ability to create child blocks that can add buttons to the toolbar after checkout success.
Steps to reproduce
Install Magento 2.1 (in any shape)
Decide that you want to add an additional button in the toolbar on Checkout Success
Investigate the template to see if it is looking for additional blocks
Become overjoyed with the ability to add blocks and insert additional buttons in this very handy space (through server-side rendering) for having them
Become saddened with the lack of such an ability, and instead add a block to appear after the success block, rendering your button awkwardly underneath the other button - or alternatively change the entire success template