This will be tough (I'd guess impossible) at this point. Adobe/Pixmantec sent out emails to all registered owners of RSP as soon as LR 1.0 was released. If you didn't get an email, I don't know how you'll convince them with this much time elapsed.
There might be something on the Pixmantec forum site.
LOL, yeah, having attempted a civil conversation with 5 or 6 of the Adobe "Customer Service" reps and gotten nothing but the royal run-around, I can tell you it's tough all right.
Both the Adobe web site at the URL in my original post, and the pixmantec forum referenced on that page still say that RSP owners will get a free DL, and there's no mention of a time limit. In fairness, it does say "1.0", but (on the pixmantec forum) it also says that LR updates for RSP owners will be handled "the same" as for anyone that paid for LR.
Slightly off topic, but why does Adobe insist on performing customer service over the phone, instead of via email or with their web based tech support system? It would be so much easier to just email screen shots of their web site, with the relevant words highlighted.