Based on other answers (see this or this) SPFile.GetFile(string) cannot be used to get hold of a "SPFile" in the _layout folder.
There are other way to read the page (like some answer suggested), but in the end you would just obtain a stream/bytearray or such - you are trying to add a web part, so I fear that wouldn't really help. That is because as far as SharePoint is concerned, _layout is a virtual IIS folder, and file inside it AREN'T seen as SPfile.
That said, adding a web part to an application page as far as I known isn't even supported: if you try to add a web part zone with a web part inside you should receive an error similar to "“Unknown server tag WebPartZone" (see this blog or this answer from Dave). Web part on application page are possible only if used as standard web control (and even there there are some issues with caching and such).
If you have to, your best bet seems to be opening the file programmatically like a text file and then adding the required tags manually - you won't be able to use the web part manager. Anyway, I would try and see if I can redeploy that page to a page library or such and transform it to a standard publishing page.