Finally got hold of a BBC World clip of the Ford Focus RS test via the Wayback machine. This, coupled along with the Noble M12 test in that season's "Best-of" compilation, means I can now name a majority of the episode's ORIGINAL, pre-butchered soundtrack, mostly thanks to Soundhound. Unfortunately, the old Ford-related stuff during the last 15 - 20 minutes remains unresolved, as do two of the tracks which Clarkson talked over too much for the app to get a good sample from.
Timestamps are given for the Motortrend Online version of the episode, as that is the version I will re-dub for TGCC v2.0.
05:51 - 06:44 - Band of the Welsh Guards - Rhyfelgyrch Gwyr Harlech
07:17 - 07:34 - Rae & Christian feat. Veba - Swan Song (For A Nation)
07:57 - 08:08 - Unknown
09:47 - 10:14 - Hybrid - Finished Symphony
10:21 - 11:02 - Unknown (parts sound VERY similar to Lemon Jelly's "Come Down on Me", but that was released in 2005)
11:24 - 11:31 - Band of the Welsh Guards - Rhyfelgyrch Gwyr Harlech
23:22 - 27:06 [Intermittent] - Mo Solid Gold - Personal Saviour
28:33 - 29:56 [Intermittent] - Doris Day - Dream a Little Dream of Me (Remains in all cuts, albeit possibly muted)