I added some additional logging to my node and ran it for a few days.
There's a pull req open for my extra logging, it is quite trivial. Here's
what it looks like:

2013-11-21 13:41:04 AcceptToMemoryPool:
5.9.24.81:7834/Satoshi:0.8.99/Gangnam Style:2.1/ : accepted
2d1bbcc2bf64dfcb57a2f0180b2607a48a34de4422c446929b26b190083bbfe7 (poolsz
2087)
2013-11-21 13:41:05 AcceptToMemoryPool:
198.12.127.2:29057/Satoshi:0.8.99/Gangnam Style:2.1/ : accepted
28bb94978bdaa224faeafa95d03a0c4f5743396d6f592469c5ac2b64184ac716 (poolsz
2088)
2013-11-21 13:41:06 ERROR: AcceptToMemoryPool : nonstandard transaction:
dust
2013-11-21 13:41:06
42323d9553e4c592d27765dc3ef9152c186cb7d67b08d783d72974a56085032d from
82.68.68.254:39232 /Satoshi:0.8.1/ was not accepted into the memory pool:
dust
2013-11-21 13:41:06 AcceptToMemoryPool:
198.12.127.2:29057/Satoshi:0.8.99/Gangnam Style:2.1/ : accepted
2fdb19e5e87d518b7b6bb7371d547a5f60c2bb056ba4522190460f0bc41b51fb (poolsz
2089)
2013-11-21 13:41:08 AcceptToMemoryPool:
5.9.24.81:7834/Satoshi:0.8.99/Gangnam Style:2.1/ : accepted
52c8ed6a48f89d48b1152b67ac0b718a7aadb5f9a0c70c18b9b2fed058ca3323 (poolsz
2090)
2013-11-21 13:41:08 AcceptToMemoryPool:
198.12.127.2:29057/Satoshi:0.8.99/Gangnam Style:2.1/ : accepted
980bbdbd4a6b365fa6f13fb5247eb6cb1e54847e490c3b7c3026d1548fb9efc6 (poolsz
2091)
2013-11-21 13:41:08 AcceptToMemoryPool:
64.120.253.194:60896/Satoshi:0.8.99/Gangnam Style:2.0/ : accepted
03f79c611bbdc1afa7afa67eb0bbd4d8bc86a730a7066622e2709ae506e61e0f (poolsz
2092)
2013-11-21 13:41:10 AcceptToMemoryPool:
5.9.24.81:7834/Satoshi:0.8.99/Gangnam Style:2.1/ : accepted
af8096ad637af1ca022a5146e07cf1fc6bfbec877935f9e114b279fcfe26c06d (poolsz
2093)
2013-11-21 13:41:10 AcceptToMemoryPool:
5.9.24.81:7834/Satoshi:0.8.99/Gangnam Style:2.1/ : accepted
751c2415d058d45ca602fdf1b6490edb6e57fc718e914d628c11b17e25aac834 (poolsz
2094)



Despite that I have 87 connections from regular nodes, virtually all
transactions seen by my node are being announced by this modified software,
which appears to run on several different machines.

I am wondering if anyone out there knows/owns these nodes and if they are
relaying transactions without checking their validity. That seems the most
likely reason for how they are always able to win the race to be the first
to announce to my node.