It may sound trite, but it's actually true: You can't impeach someone who isn't eligible to be President. If they're not eligible, they're not President, thus impeachment isn't a solution. Only solution is a Quo Warranto demand, which has been filed, but not acknowledged by any DC court yet. Maybe never will be. That's the problem. Going through any kind of judicial or procedural process depends on the convening body being free of corruption and/or lack of spine. Still,the above link is an interesting read, even if it is just another dead end.