So I have been transcoding the rest of the series into 720p, but the loss of quality is visible. And I didn't want to transcode anymore -- otherwise I could have kept the old MACH F around!
I use the Combined Community Codec Pack, which in turn installs ffdshow to handle the video codecs, which in turn uses the open source libavcodec library to do the actual decoding. While it gets the job done, it's not noted for it's efficiency, so there was a possibility that installing a more efficient codec would help the poor overworked MACH F with full HD streams.
Some research suggested that the payware CoreAVC would do the trick. I read through the site, and it makes much of the use of NVidia GPU accelleration -- but I have an ATI chipset in the MACH F. I downloaded an evaluation version (*cough*) and installed it. And to my surprise, CoreAVC managed to decode the full HD stream without any problems -- even the high-motion scenes didn't give any problems!
There's this shot in the opening sequence of Shangri-La that's a quick zoom-out of a forest, which has lots of details and lots of motion. With libavcodec this was the part where sound and video would de-sync, but with CoreAVC it played on without as much as a hiccup!
So I went to the site and bought a license to the codec -- it's only USD 10, and it saves me a lot of hassle. And my salary is paid in part by the sale of software, so I want to return the favour to others who are dependent on software sales for their income.