Ok, I've taken some more measurements, but let me address the other questions real quick. I'm using a SpeakerPower amp (2400 watts RMS) that only has one filter for subs (30-80Hz), but I am not using it. I did engage the filter real quick and it showed as it should in the measure that followed. So, I'm pretty certain the amp is running full frequency (and the AVR is taking care of the crossover). The internal volume of the sub after accounting for bracing and the subwoofer is just over 3.25 cu ft.
After taking the measures that you requested, it's looking like there is definitely a problem with the sub location. In fact, with the sub only and no mains, the 28Hz dip now looks much more like a null to me. I guess even with the crossover set to 80Hz, the roll-off was such that the mains still helped reduce the dip at 28Hz.
Also, when the sub was facing backwards, the 28Hz dip still had a serious presence.
Here's the graphs. Sorry again that the pics aren't turning out to great.
Sub Only - Mains disconnected - Measured at the LP and 1 foot in front of sub (I guess it's pretty obvious which is which!):
And here is the original graph with 1/3 smoothing applied (this had the mains running as well):