It indeed cannot replace search bars automatically, that does not utilize the searchform.php theme implementation method. Most themes do that, but there are a few exceptions.
In this case the only possible option is to directly replace the search code within the theme code. There is no generic place of this search code, so I'm not able to tell you where to look and what to replace exactly. I highly suggest contacting the theme developer, he will know exactly which files to approach and safely change.
The method is basically to locate the theme file where the search bar is included or printed, and replace that with the PHP version of the shortcode: https://goo.gl/8NlmBq
While it's not part of the support process, I can try changing it for you – if you have a test environment which I can temporarly access via FTP.
In this case please also specify where the original search bar is on your website visually, if it's not in a visible location.
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