I'm afraid there is no other way. The plugin executes extremely fast, way below 0.1 seconds, so it's optimized to the maximum already. And the P3 profiler is not going to help in this case, because ajax requests usually act very differently from a page loading process.
It's not possible to force other plugins to not load programatically unfortunately, so the search handler must wait for it's turn. I've written an article about WP performance, you can read it if you want to, but the cause in your case is the very high number of plugins.
You can turn on caching on the caching options panel, but it's not going to help much, because the plugin gets the results almost immediately. The cached handler is still going to get held up by the WP loading process.
Unfortunately I'm not doing freelance or contract jobs right now.Best,
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