Hi Mike,
This can be quite misleading. The 3803 simply converts the signal from one form to another, rather than upscaling as many DVD players, and some amps now do. All signals will be output as the same resolution as they are input, the only difference being that the amp allows you to have a single component connection to you projector. So 576i/480i input on composite or S-video, will output the same via component.
I owned a Denon 3802 for many years before recently upgrading to the 3806 and on that model it was necessary to run two connection to the projector, one for component, and a second for S-video.
For your setup, I would use the Denon to switch sources, and then run them to the projector via the line doubler, this would then allow you to use the doubler to optimise all sources.
Hope this helps