First you can try disabling animations, i.e., setting the animation speed to ‘Instant’ (System Settings → Workspace Behavior → Animation Speed). Then the launcher will appear much quicker when you press ‘Start’ / the ‘Meta’ key.

Then you can try disabling some search plugins. To the right of the search field in the launcher, there’s a settings icon. Click on it and then on the ‘Configure Enabled Search Plugins…’ button. (The name of the button is misleading; you can also disable plugins here.) A good strategy is to first disable all plugins and see if this helps. If it does, enable each plugin you need, one by one, until the search becomes slow again.

I know this is not really answering your question but I use yakuake on KDE, which is a drop-down terminal, and it uses F12 as the shortcut to open. Very fast, no hassle. Depending on how you set it up you can exit by F12 again, or it will hide when it loses focus i.e. you click somewhere outside of it.

Weird. It's always been fast for me.

Is something throttling your CPU ? Have you tried using ALT+F2 to search ? But even if you had not it should be quick to search...