Those who have a broken Rock Band stratocaster can visit Electronic Arts' customer support website and they "will send a replacement immediately." We have yet to get the site to work for us (curse you, "Diagnostic code: page WWN, 2:") but hopefully that will be cleared up soon. The impatient and handy people out there can also try a more DIY fix (thanks, Oxide99).
The post also tackled the subject of PlayStation 3's guitar compatibility woes. Though not mentioning the Guitar Hero III Les Paul by name, they do say that they read everything in the forums posts and that they are "committed to providing the best play experience possible and working hard to ensure that we solve these problems as soon as possible."
Read - Rockband [sic] Support
Read - PS3 Guitar Compatibility; strum bars