New .03/.05 data:

The disturbing thing is that the oscillations fall off, then come back with the opposite sign. While I'm tempted to just truncate the data at timeslice 15, I have the nagging feeling that the data past there might be the true ground state, while the data earlier could simply be an excited state. Do we have a physical reason for believing that the ground state has a coefficient with a positive sign? If so, that would justify truncating the data.

Ok, adding more data fixed the problem, leading to the effective mass plot:
Configs 000-544:

However, what caused such a strong signal with the early configurations? Here's a series of plots taking the configurations 100 at a time:

Configs 000-100:

Configs 100-200:

Configs 200-300:

Configs 300-400:

Configs 400-500:

It seems to me that there's some strong dependence on which configurations are included. Is this normal?