ckbckb, I've got the smaller brother of your AOC, the Envision L26W761, and I bet the guts of both sets are pretty much the same. Had very similar problems on our "flying saucer," pre-amped antenna in the attic once last spring rolled around. Better antennas and no pre-amp solved all issues, so I believe this HDTV is rather susceptible to front-end overload.
Try this experiment: Bypass the pre-amp and power injector and feed unamplified signals directly from the antenna to the L32 (barrel-connector splices are OK, but not the splitter). If things improve, your antenna is fine, but local signals are too strong for the pre-amp you're using, causing overload. The solution would be a lower gain pre-amp -- or maybe none at all.
We're happy with this set. As with a lot of cheapo HDTVs, though, I suspect AOC's designers cut corners knowing that roughly 17 of 20 buyers would connect the tuner to a cable or satellite service. On the other hand, CECB engineers knew that every last converter box would get signals from an antenna, many of them rabbit ears, and so they made sure their tuners would be more robust in the face of overload, multipath interference, weak signals, etc. I've installed a few DTX9950s for older neighbors hereabouts (rabbit-ears users all!), and I have to agree with you that it's got a better tuner than my L26.
Good luck trying to get anything more out of AOC than what's on the spec sheet. I emailed them a couple of times to ask about parameters such as minimum signal-to-noise ratio and minimum sensitivity to achieve digital-signal lock. No answer. I read an FCC paper not too long ago in which they bench-tested a total of about 30 HDTVs and CECBs for comparison. All the specs anyone would want are in there, but naturally, they wouldn't identify anything by brand and model, only by price range (in the case of HDTVs).