The easiest would probably to put it in Main Options > HEader > Site Title Tagline > Header Extra HTML box, and select the option “Move Extra HTML Over Header”
The positioning is done from the left (X) and the top (Y), so you should probably add the rule below to Advanced Options > HEadv Section > Custom CSS Rule box, to change the vertical positioning to a fixed bottom value (that would probably be better resposnisvely.
#header-extra-html {top:auto;bottom:10px;}
For it to work responsively the add will need to scale with the header.
Speaking of responsiveness, I hope you realize your site is not at all responsive right now. If you reduce the size of the browser, the design completely falls apart.
Starting with the fixed 300px right margin on the wrapper that should really be a percentage, and continuing with the posts that are using a table causing the post content to move out and to the left, as well as your area under the header that does not scale at all..