Thanks for the suggestions. In the MIDI, I don't see any bars (or lines).
In the Automation section, the green triangle was already off. Turning it on didn't change anything nor did turning it back off.
MOTU support had me try turning on Input Filter for SysEx events. This also did not help--I even tried filtering everything but Notes, but the results did not change.
Here's something new I noticed: if I just play the same guitar note over and over and over again, after the note sounds correctly once, it will continue sounding over and over perfectly (as long as I don't switch to playing a different note).
For example, if I play quarter notes of E-E-E-E-E-E-E-E-E-E, eventually one E will sound correctly and after that, they each continue to sound.
Similarly, if I strum an Em chord over and over and over, eventually one of the notes will start to sound, then another... until eventually all 6 notes of the full Em chord will sound over and over (unless I change chords).
Does any of this make any sense to anyone?
I have yet to try DP8 under OS X 10.6.8. (Hopefully, this weekend.) I read somewhere that there was a change in MIDI processing sometime after DP5, something to do with how simultaneous notes are processed. Unfortunately, I can't find that article now. Does it ring a bell to anyone.
Lastly, thanks again to everyone for trying to help. I must admit, I just assumed I was missing something obvious and that I'd be scolded for inexperience (if not incompetence). So, I guess the silver lining is that maybe I'm not quite as useless as I felt like I was!
(EDIT: MORE INFO)
OK, so I told my kids this DP thing was just bugging me, so we wouldn't be doing anything tonight. Instead, I went ahead and installed DP8 onto the hard drive where I have DP5 and Mac OS X 10.6.8... the results were exactly the same.
I could close DP8, open DP5 and record guitar MIDI with no issues. Quit DP5, open DP8 and the problem returns immediately. The MIDIMonitor.app shows the exact same sort of output as under Mac OS X 10.8.5 and the more recent M-Audio driver.
So, it seems that DP8 simply interprets this guitar's MIDI output differently (incorrectly?). Any ideas?