Send A Keystroke To A Window?

I'm trying to send a keystroke to a window (of an external executable) but am having problems.

If I launch the exe with a window I can successfully send it a "q" (in order to make it exit) using the follow:

1) AppActivate and SendKeys

2) SendMessage API using WM_KEYDOWN and WM_KEYUP

3) AppActivate and keybd_event or SetForegroundWindow and keybd_event

However, if I launch it without a window, obviously method 1) does not work as SendKeys only work on applications with visible windows, but I thought that method 2) would work. However, it doesn't. Also, using method 3) with SetForegroundWindow as this seems to only work with visible windows, which is not really a surprise I guess, given the name.

Another method I have tried, which won't work is using the RedirectStandardInput - I have this working correctly, but the application is looking for keyboard events, not writes to its StandardInput stream, so this doesn't have any effect.

Finally, I have tried using SendMessage and FindWindowEx, and TranslateMessage, to find any child windows or controls that should be receiving the messages, rather than the main window. However, no child windows or controls are found, and I wouldn't have thought this would be the solution given that, if the window is present, the main window receives the message as it should.

So, I have confirmed that the messages are going to the correct window, as they arrive as they should when the application is launched with a window, but I cannot get the application to receive the message when it is window-less. The solution doesn't have to involve messages, or even be particularly robust, but this is what I have tried so far (all the obvious stuff!)