Focus a window without changing z-order - c

Question

I have a somewhat hackish utility that sends keystrokes to a window, using SendInput(). That works just fine, however, the target window needs to be a foreground window, so before sending anything, the utility needs to call SetForegroundWindow(). This is annoying from the user's perspective, as the target window flashes to the top (even though the utility immediately switches back to the recent active window, so that the user can continue work).
Is there a way to focus a window, without changing z-order? I realise that it is not a common use case, as it would be extremely frustrating under normal conditions for the user to have a background window active, where they might not even see what they are typing. I tried using both SetFocus() and SetWindowPos() with SWP_NOZORDER, but neither of them actually activates the window.
Note that the window I'm trying to activate is not owned by the calling thread. Also note that I can't use SendMessage() as the keystroke is a CTRL+NUMPAD3 combination and the target window will not react to separate WM_KEYDOWN / WM_KEYUP events, I've tried. It might be relevant that I'm trying to use this on Windows 7.
My code so far is:
HWND h_target = FindWindow(...);
INPUT p_input[2] = {0};
p_input[0].type = INPUT_KEYBOARD;
p_input[0].ki.wVk = VK_CONTROL;
p_input[1].type = INPUT_KEYBOARD;
p_input[1].ki.wVk = VK_NUMPAD3;
// prepare input
HWND h_act = GetForegroundWindow();
// remember this
SetForegroundWindow(h_target); // works
//SetWindowPos(h_target, HWND_TOP, 0, 0, 0, 0, SWP_NOMOVE | SWP_NOSIZE); // does not work
// activate the target window first
SendInput(2, p_input, sizeof(INPUT));
// send the keystrokes
p_input[0].ki.dwFlags |= KEYEVENTF_KEYUP;
p_input[1].ki.dwFlags |= KEYEVENTF_KEYUP;
SendInput(2, p_input, sizeof(INPUT));
// don't forget to release the keys
SetForegroundWindow(h_act);
// put the active window back