I am having a difficult time getting the latest version of EAC, with its builtin version of AccurateRip to get calibrated with the DVD drive of my computer.

Doing a web search on my DVD drive found this posting on the EAC website where someone else reports essentially the same problem:
http://www.digital-inn.de/131062-post19.html

For both of us, inserting key discs always results in inconsistent offset measurements. Thus, AccurateRip can never be activated.

Is there any hope here, or are some optical drives simply hopeless for use with AccurateRip?

101 Error

Yes, there are a few drives that do not have consistent offsets and thus cannot be used with accuraterip (and probably should not be used by anyone that would want to use accuraterip either)

I haven't looked over that post at digital-inn very carefully, but it seems that none of the discs are from the same pressings that were used as key discs.

The only thing I feel good about suggesting is to try to find a different one.

If you find that the same disc gives different results between attempts then your drive isn't capable of delivering a consistent offset and should not be used for ripping. I happen to have a drive that AR refuses to configure even though I have a set of key discs that work with other drives, and this drive does deliver a consistent offset. The drive is an old ASUS 50X CD-ROM. Someone else has reported the same problem with it as well (I think)...
http://www.audiosense.org/forum/showthread.php?t=228

I doubt that either of these are happening in your situation, though.