I'm still attempting to confirm my hypothesis that this problem may be isolated to servers hosted on the same physical Hyper-V host, but certainly at least I've found frequent, though intermittent, cases of attempting to ping some of my servers from some of my other servers, and getting bizarre responses. The standard Windows ping tool will instantly (as in far, far faster than you would expect for a < 1ms reply time) report all four replies, with numbers in the tens of thousands of ms.
Running ping -n 1000 fs1.nisgaa.net > ping-fs1.log
completed in about 10-15 seconds.
1. The first line: Reply from 10.3.0.17: bytes=32 time=85546ms TTL=128
2. The next ~450: Reply from 10.3.0.17: bytes=32 time=63979ms TTL=128
3. The next two: Reply from 10.3.0.17: bytes=32 time<1ms TTL=128 (these lines actually take a second to spit out, unlike the above, which appear instantly)
4. Next two: Reply from 10.3.0.17: bytes=32 time=85546ms TTL=128
5. Next two: Reply from 10.3.0.17: bytes=32 time<1ms TTL=128
6. Next one: Reply from 10.3.0.17: bytes=32 time=63980ms TTL=128
7. Next five: Reply from 10.3.0.17: bytes=32 time<1ms TTL=128
8. Next three: Reply from 10.3.0.17: bytes=32 time=91472ms TTL=128
9. Next ~75: Reply from 10.3.0.17: bytes=32 time=63980ms TTL=128
0. Next four: Reply from 10.3.0.17: bytes=32 time<1ms TTL=128
1. Next one: Reply from 10.3.0.17: bytes=32 time=85546ms TTL=128
2. Next one: Reply from 10.3.0.17: bytes=32 time<1ms TTL=128
3. Next one: Reply from 10.3.0.17: bytes=32 time=85546ms TTL=128
4. Next 15: Reply from 10.3.0.17: bytes=32 time=63980ms TTL=128
And so on, with large, repeating chunks that it claims take minutes, but are reported instantly, followed by a small handful of < 1ms responses, as I would expect.
Any ideas at all what could cause something like this?