Hello Adam,
You can try applied this CSS hack in your template CSS file and see how it goes?
div#discuss-wrapper .discuss-searchbar .discuss-avatar {
display: none;
}
div#discuss-wrapper .discuss-searchbar--select {
width: 200px !important;
}
If still can't meet your requirement, is it possible provide us with your Joomla backend and FTP access so we can help you check on this? Please advise.