The Button element maintain a certain HTML structure and classes in the Tags, which is not present in your shortcode. I went ahead and added the HTML tags and the classes to implement the similar style of the button in Header. I have found the style has been integrated with specifiec class named e209-12, which is added statically to maintain the styles. The X Button code will look like the following.
[x_button href="https://whyfire.com/scenarios-page-salters/?refdealer=template-price-book-salters" class="e209-12 x-anchor x-anchor-button x-hide-xs"]<span class="x-anchor-content"><span class="x-anchor-text"><span class="x-anchor-text-primary">GET MY ESTIMATE</span></span></span>[/x_button]
I have also removed the padding for the default class integrated for the X Button shortcode with the hierarchy class by adding the following code into the Theme Options > CSS.
Hope this helps.