It is working fine now and I did not change a thing to my configuration. Might be tv-viewer or another tool I've been using set the resolution to 384x288, but I can't reproduce that behavior anymore.
Reason why I'm using the analog part is due to the services available here in Belgium. DVB-T and DVB-C (although not supported on the HVR-1900) only give me a few free-to-air channels, analog is still the way to go if you don't want to be locked-in by one of the telco's.
The system is working fine now. I only had to disable the DVB-T part in the kernel module in order to have TVHeadend recognize the analog tuner.