I actually got a phone call from TI today after my second email complaining about my inability to complete the order on their web site. I didn't quite get the explanation for the problem, but the good news is that they took my order over the phone. I was told they would allow up to five units per order, so I took three. Apparently there are 6000+ units on backorder.
There was also a long and complicated explanation of how the initial reservation on my credit card would include a $25 shipping fee, but this would be reversed as soon as the order is shipped. Lets see how that one works out...
Overall I am quite impressed that they bothered to come back to me (with a long International phone call) at all for such a minor order. I am not used to that level of service where I come from.