Your Haupauge 950Q usb tuner supports HD up to 1080i.
The only way to increase the video quality would be to use a HD set top box. The modes on the boxes can usually be changed from 480p, 720p, and 1080i. Since those boxes have DVR functionality, that feature becomes redundant. There's also the monthly fee of anywhere from $10-$18 monthly. That depends on your area of course, if its available, etc. It probably wouldn't hurt to pick one up and at least give it a run for a month. You could then decide which device's DVR functionality you like and prefer more. The set top box's HDR of course is completely inaccessible outside of viewing it directly from the box's output, so there's no backing it up or sharing, or anything fun like that. Many of the HD boxes also have multiple output options, like dvi, hdmi, d-sub, component, rca... You might find connecting it directly to the monitor, with an adapter if necessary, might also be an option. Your monitor has d-sub and dvi, so you'd use the monitor's menu to switch between inputs. Cables boxes also have a tendency to be huge too so that's a factor as well. I was in-between televisions for awhile, and I had a HD cable box connected directly to my computer's monitor. It worked really well displaying the 1080i signal on the 1080p monitor. I realize you have a 1680x1050 monitor but it should be a simple matter of trying the modes on the cable box, and the monitor settings, if you went that route.