QAM is available on many cards like the 1600, 1800, ATi 650 and is the equivalent of most 'cable cards' in North America where premium service decryption has not be offered by cable companies TMK. It also depends on the provider, in Canada almost all of the HD cable channels are encrypted with the rare exceptions, for me it's just Discovery HD and CBC HD that are free for Toronto it's like 6-10 (but they have OTA channels as well), and a bunch of SD channels.
That is the best way to record HD content, it avoids alot of the issues and offers pretty good direct recording without the compression artifacts of most analogue capture cards. But it does depends on what channels you're trying to record and the cable company.
With the resolutions you're talking about most capture cards involve very heavy compression to record the 720P/1080i content.
Black Magic makes some nice cards I've seen in action for low compression via component and HDMI, but none of the quality HD component recorders are cheap, and many still look blocky after running compression ontop of the decompressed to analogue output of the cable box.
For you I'd say this is likely your best bet, using slightly higher compression of H.264;
http://www.hauppauge.com/site/products/hd_pvr.html
It's a pain, but it's cheaper than the truely good solutions, and it'll at least let you record what you're still looking to record.
BTW don't think the cable box can't figure out if an analogue connection is connected or not if the cable company wanted to they could've had that feature added, just like Macrovision protection on VCRs which was all analogue connections.