Hey koshman,
About the AveryTV tunner card, I'm not sure but with this gadget, it seems it would be possible; take the s-video out from the Amiga, connect it to the s-video in on your capture card and have look. Most LCD TVs have s-video in-s on them if not a couple.
An Amiga on s-video can look really good from some youtube stuff I've seen.