I tried to contact them at that link, only to get an auto-reply saying that as they theme wasn’t bought on my account, they couldn’t help me and the ticket was closed. I did say in the message that the site was assembled by an outside company so of course we were not the buyer, but that didn’t seem to matter.
Anyway I did some fiddling, and came up with the solution. I used the following CSS to hide the banner as it comes in when scrolling down;
header.site-header {
position: static !important;
}
Then used the MyStickyMenu plug-in to pin the blue menu bar to the top so it wasn’t still forced down by a now-invisible header. Thanks for your help!