Must I shell out the $$$ for a dealer-issued fob?

You can program a silver logo sks key to start(insert in slot) your none sks car. The doors will not work. Different frequency. Look at your key, it should have an all black logo on the back. Ive programmed over 50 prius smart keys and have seen it all. If you do have a black logo, most likely its a stuck button as an earlier member noted.
The same for a black logo key starting an sks car. It will work but doors wont. Both systems use the same chip inside.