How to immediately hide voicetext or put GUI over voicetext?

[iamlowlikeyou]

I'm working on a pause function, where the screen is getting "greyed out" with a half transparent GUI.
I would like eventual speech text (if in the middle of a dialog) to be either "behind" the grey GUI or simply to become invisible...
I have tried both changing the speech font to an invisible font with a command, but that only works for subsequent dialogs, which means that the text that is already on screen stays the same font, and thus stays visible. I also tried setting the VoiceMode to voice only, but that doesn't seem to work when there is no voice file (besides I'm not sure that would clear text already on screen either).
Is there any way to make invisible text that is already at screen?

I haven't managed to find any possible way to put the GUI over the text yet, I'm not sure if that's possible?