How important is it to try to get copies of the fraudulent applications/materials used by the thieves? This appears to be a consumer right according to the FTC, but the companies seem not to want to provide it and can deny giving this info to the victim in some cases (for this Experien references this government site with links in a letter). I'm wondering if this is worth all the back-and-forth with the fraud departments of the companies or if this kind of information is much less important than just taking precautions, filing police reports, credit monitoring, etc.
The only reason for you to ask for it is so that you could forward it to law enforcement if for some reason they cannot get it on their own. You may be able to identify the thief if it is someone you know (recognize the hand writing, style, address, phone, etc) and report to the detective handling your case. Other than that - not much use to you.