I have an HD-supporting TV Tuner that I use with an HD antenna to get local, digital HD signals.

I just bought this Upconverting DVD Player for $24.99 (Google coupon, mind you); my TV Tuner does not have HDMI input, however, so if I run it Composite (RED/YELLOW/WHITE) that would go back to analog and lose the purpose.

Is there any way to get crisp, HD-upconverting video on DVD's onto my 22" Acer flatpanel?

If it is really an HD tuner, it should be able to take Component in, which gives you the picture quality of HDMI. That said, S-Video should give you about everything the DVD has to offer, as upscaling just scales it up, it doesn't increase the quality.