I was flipping through the forums for the umpteenth time today and stumbled upon something I hadn't seen suggested before.  The user's name is "ibenjamin" (or something similar) and he listed a few additional reasons that the integration may not be working besides what has been widely reported.  The first was the use of "Call Tones", which I had seen suggested elsewhere and didn't apply to me.  The second, and this was the issue for me, was having numbers blocked via Sprint.

My account is not corporate or government, and I receive no discounts.  I am also current on my bill, so I, nor the several Sprint employees I spoke to could figure out why my account wasn't eligible.  This was the reason.

I had "blocked", via Sprint's website on my account, a certain telemarketer's number that I was continually receiving calls from.  As soon as I removed that, I waited 5 minutes, and low and behold, I can now integrate.

So, for those who don't fall into the Discount/Corporate/etc issue categories, make sure you have no numbers blocked on your account.

Thanks to the poster who originally put this up.  Unbelievable that it was something as simple as that, yet the answer was found buried in a forum.