hmmm....well, let me be sure I understand, you are just trying to get a TV signal to the monitor, correct...?
If yes, I would probably just go buy a length of coax and replace the HDMI as I don't know of anything inexpensive that will do what you need....plus, once converted to HDMI, I am not all that confident your tuner will recognize it as a signal source that it can scan for channels...if your intent is to watch tv, this might be a problem.
Short of having the tuner in the back where both the coax input and HDMI output are located, I can't think of another option....