I tried the transfer rate scan, and it was a smooth ascending line that looked more or less identical to the top picture that you posted. There were no drops whatsoever.
I decided to try burning a disc again, and I again got the same problem during the verification phase (slow as molasses read rate, estimated finish time of well over a day).
I then took out my Blu-ray burner, put in the OEM DVD Burner that had originally come with my computer, and tried burning the DVD again. This time, everything went off without a hitch - even though I used a disc that I knew to be defective (it had a visible blemish, which the burner cleverly wrote around). I then tried a second time with what I believe to be a good disc, and everything again worked perfectly.
So it appears extremely likely that the LG Blu-ray burner is indeed the source of the problem, as the other DVD burner handled the same task perfectly twice in a row (even though one of those times was with a flawed disc).
I do find it weird that the only time that problems seem to present themselves with the Blu-ray burner is during IMGBurn automatic verification sessions. Even manual verification sessions seemed to work fine. It's just whenever IMGBurn cycles the tray and starts a verify session right after burning the disc. It did still have the problem during one manual verification session that I started, but that was while the same IMGBurn window was open from the last write/verification session. When I restarted IMGBurn and ran another manual verification, it seemed to work fine.
But since I've never had this problem repeat itself so many times in such a short time period before, it still seemingly points to a problem with the drive. I think that I should probably start looking for a new Blu-ray burner.
Do you happen to be well-acquainted with any particular Blu-ray burners? That is to say, are there are Blu-ray burners that you could advise me on regarding merits and problems?